The Football Association handed down a hefty 10-game suspension on Suarez after it found the Uruguayan guilty of violent conduct following his bite on Chelsea defender Branislav Ivanovic.
The suspension, one of the largest meted out by the FA, came 16 months after Suarez was banned for eight matches for racially abusing Manchester United's Patrice Evra.
Given that Suarez thought he should be suspended for just three games for the biting incident, many had speculated that the 26-year-old would take the news badly and push for a summer move away from Anfield.
Suarez has certainly attracted many suitors after scoring 30 times this season, but Purslow, who helped bring Suarez to Anfield from Ajax, is convinced the 26-year-old will stay.
"I don't understand the link between a disciplinary issue and whether a player should be at the club or not," Purslow said at the BT Sports Industry Awards last night.
"A player commits an offence, you discipline him, and then the authorities might discipline him. That is the issue.
"What has that got to do with whether Luis Suarez should be playing from Liverpool or not?
"He is easily the most effective and important player in the team. He is enormously valuable.
"What would a commercial enterprise get from getting rid of their most important player, probably at a discounted price, because of a disciplinary problem?
"No football club in the world would do that."
Although Suarez's bite on Ivanovic, which came on the meeting between the two sides on April 21, sparked major criticism of the player, many were not expecting the FA's punishment to be so tough.
"I thought it was a very harsh ban," Purslow added.
"It was probably more than most of us expected, but that should not diminish in any way the seriousness of the offence.
"It was a terrible incident, a very unusual, graphic, and unappetising incident."
Liverpool proved they can cope without Suarez last weekend when they hammered Newcastle 6-0 at St James' Park.
The Reds are finishing the season on a positive run, further easing doubts about the ability of Brendan Rodgers, who swapped Swansea for Anfield in the summer following the dismissal of Kenny Dalglish.
A top-four finish is out of Liverpool's reach, but victory in this weekend's Merseyside derby will put the Reds within two points of neighbours Everton, who sit in sixth position.
"Results have been generally improving and we are playing an exciting brand of football," Purslow added.
"Everything came together last weekend and I think we are ending the season on a really positive trend.
"Brendan has made a good start. It was a massive step up from what he did previously. You are hiring a young, improver and he is going to learn and improve as he goes along and I think certainly for a first season, given how much of a step up he made, and given the amount of change at the club, he has done pretty well.
"A new manager and new players need time. At the start of the season we were probably looking at finishing between fourth and seventh and that's the way things are going to work out."