Bolton midfielder Muamba is in intensive care at the London Chest Hospital after he collapsed during the Trotters' FA Cup quarter-final at Spurs.
A number of Tottenham players were visibly distressed at the 23-year-old's collapse and they have requested that they be checked to see if they have any long-term heart defects which could affect them in the future.
"The players have all demanded cardiac screening today [Monday]," sports cardiologist Sanjay Sharma told Sky News.
"That involves taking a history relating to cardiac symptoms, which include chest pain during exertion or breath which is disproportionate to the amount of exercise being performed and blackouts, (and) asking about a family history because many of these conditions that can cause cardiac arrest are hereditary.
"We then perform a cardiac examination and following that we do an ECG (electrocardiogram) which is an electrical tracing of the heart which looks for electric faults of the heart and a cardiac ultrasound which looks at heart muscle problems or problems with the heart values."
Tottenham manager Harry Redknapp backed the move, saying: "Fortunately, we already had a cardiologist visiting the training ground today [Monday] for routine screening, so we are able to offer any player who wishes to be tested for the purpose of reassurance an additional opportunity to be screened."
Redknapp also described Muamba's collapse as "horrendous" and conceded that Saturday's game bore an eerie resemblance to the collapse in 2003 of Foe, whom he signed for West Ham four years earlier.
"Marc was a fantastic player," said an emotional Redknapp, who was speaking at a Gillette Soccer Saturday Roadshow event in Bournemouth tonight.
"He was playing for Cameroon in France and he collapsed on the pitch and we lost him.
"He was a great character, a great boy, so please God, we hope that Fabrice will recover well and we are all keeping our fingers crossed.
"It felt like it was similar to that game (where Foe died) at the time on Saturday. The lads said his heart had stopped and we really were thinking... you know... it was an unbelievable experience.
"I wasn't there when Marc collapsed. It's the first time I'd seen that happen. It was unreal, but the right people were there to support him."
The 65-year-old, who underwent a minor heart procedure last year to unblock two arteries, is encouraged by the small signs of encouragement from the former Arsenal man.
"I was just so pleased because really I haven't been able to think about anyone else all weekend," Redknapp added.
"When we were there on Saturday night it was just a horrendous situation.
"Everyone really feared the worst at one stage.
"I just remember seeing him laying on the floor. My first reaction was that someone had elbowed him off the ball.
"Then someone said he had collapsed and once we saw them pumping his chest, we just knew how serious it was.
"The medical staff were just amazing and he is such a strong, fit lad and that has been a big help for him I think.
"We pray for him and wish him all the best. We hope he can pull through."
Tottenham confirmed that their home game against Stoke will go ahead on Wednesday despite Muamba's collapse.
Redknapp admits some of his squad may take time to get over the incident, but says the club will offer any assistance they can to help them.
"What happened on Saturday to Fabrice Muamba was a shock to everyone," Redknapp told Tottenham's website.
"It is possible that the effects of this could hit some quicker than others and, despite these difficult circumstances, we all have to pull together and carry on with our season.
"We will be providing players with whatever support they need in order to help them move on from what has happened, while obviously always keeping Fabrice at the forefront of our minds and willing him to make a recovery."
Spurs striker Jermain Defoe was left in tears at seeing his friend collapse on the pitch on Saturday and visited him at the hospital in Bethnal Green, east London, to wish him well.
Other Tottenham players were seen praying for the former Arsenal man as he lay receiving treatment on the pitch.
Spurs forward Rafael van der Vaart recalled the event with sadness, telling his official website: "It's almost incomprehensible what has happened.
"(It was) simply horrifying to see such a young player on the ground struggling for his life.
"I was standing about 10 metres from him but I didn't see him fall. It happened behind my back, but when I turned I immediately knew things weren't good.
"At that time all players on the field felt the panic as well. It was horrible to witness, it's the absolute low in my football career.
"I'd like to express my sincere support to the family, team-mates and everyone who is involved with Bolton Wanderers.
"Fabrice, we'll keep praying for you and I hope with all my heart that everything will be all right again."
Tottenham defender Benoit Assou-Ekotto, 27, also spoke of his shock at the incident, which reminded him of the game in which fellow Cameroonian Marc-Vivien Foe died in 2003 after collapsing on the pitch during a game in France.
"Saturday was one of those days that will stay with me forever," Assou-Ekotto wrote in his London Evening Standard column.
"When I saw him lying on the pitch at White Hart Lane, I was scared. Scared for him, scared for his family, his friends and all those people who know him and who care about him.
"I was also scared because he was just like me. He is young, supposedly fit - an athlete - who a few seconds ago was running up and down the same pitch as me. I had flashbacks of what had happened to my countryman, the late Marc-Vivien Foe.
"You want to stop these thoughts but the pictures keep coming into your head and I must say I was scared. Scared as I wondered how it could all just end like that for a young man? I could see the same questions in the eyes of my team-mates, the Bolton players, our bosses and their colleagues."