Sherwood, who replaced Andre Villas-Boas as Spurs boss in December on an 18-month deal, has spoken of his fear of being replaced and Louis van Gaal has been linked to the White Hart Lane post.
Van Gaal, who is to step down as Holland boss following this summer's World Cup, gave Mourinho his chance in football, appointing the Portuguese as his assistant boss at Barcelona.
Mourinho, recognising his own position as a foreign Premier League boss, recently suggested British managers should be given a chance, which Sherwood has.
"Now it's up to Sherwood," Mourinho said.
"He has a chance. A chance that lots of people are waiting for. Now it's up to him."
Chelsea play Sherwood's fifth-placed Tottenham on Saturday bidding to extend their advantage at the top of the Premier League to seven points.
Teams managed by Mourinho, a championship winner in Portugal, England, Italy and Spain, have never relinquished a lead held in March, but he believes the table is false as come Saturday night Manchester City will have three games in hand.
"At this moment, I'm not top of the league," Mourinho said.
"I'm top of the league the day that I have the same number of matches as all the other teams and I have one more point than all the other teams.
"If that day arrives, I can say I'm top of the league. Until that moment, if other teams have matches in hand and can win and be top of the league, which is the specific case of Manchester City, they are top of the league."
The Portuguese also praised the approach of fourth officials this season, despite incidents such as Newcastle boss Alan Pardew's headbutt on Hull midfielder David Meyler.
"This season, I'm having good experiences with the fourth official," said Mourinho, who is friends with Pardew and spoke to him in the immediate aftermath of the incident.
"It's easier to behave in this country. The communication is also much easier.
"They're not going there like a policeman. They know very well how to calm situations.
"I found myself two metres on the pitch in a home match. Is that a reason to be sent to the stands? Yes. But the fourth official told me 'Jose, you cannot be here, sit down'. 'I'm sorry mate, you are right'."
The situation is better than in Spain, where Mourinho spent the past three seasons with Real Madrid.
He added: "The first way is that in Spain, I'm Portuguese. That's the most important thing.
"The second thing is the communication is not the same. If you make a mistake, you are out.
"Here the communication is good."