Redknapp was admitted to hospital on Tuesday night to have tests after he started feeling breathless while running.
The Spurs boss had two stents inserted the following day to help unblock two coronary arteries and he was ruled out of the club’s Europa League trip to Rubin Kazan.
The 64-year-old will now rest for the next two weeks and assistant manager Kevin Bond will manage the team in his absence.
Redknapp is thought to have watched the Rubin game from his Dorset home and the former West Ham boss will do the same again this weekend as his team look to extend their unbeaten run to eight matches at the home of their London rivals.
Redknapp was in chipper mood when he spoke for the first time since the procedure yesterday and now Gallas has called on the Spurs squad to broaden the smile on their manager’s face by registering their seventh win in eight games this weekend.
“We have to win because he is not well at the moment,” Gallas said.
“The manager is a good guy so I think we have to do a good job on Sunday for him.”
Gallas played 70 minutes of Thursday night’s defeat in Kazan after making a recovery from a calf injury which had kept him out of action since the end of last season.
The Frenchman admits it was hard to watch on as his team-mates were easily beaten in their opening two league games against Manchester United and then against Manchester City.
But since the 5-1 defeat to Roberto Mancini’s men, Spurs have taken 19 points from a possible 21 to move level with fourth-placed Chelsea, who have played once more than their north London rivals.
Last season the club fell six points short of qualifying for the Champions League after a mid-season stutter, but Gallas, who was a regular in defence last term, thinks the squad has a better chance of finishing in the top four this year. “The squad is stronger this year,” he said. “We believe we can finish in the top four and maybe win something.
“Everyone is talking about (league leaders) Manchester City. They are doing well, but I think we have to believe in ourselves and try to win every game and at the end of the season, we will see.”
Tottenham’s recent good run has coincided with the signing of Scott Parker and Emmanuel Adebayor just before the transfer window closed.
Adebayor impressed by scoring three goals in his first two matches while Parker has been in sensational form since moving across London from West Ham in the summer.
The England midfielder put in a lionhearted display to win man of the match against QPR last Sunday and Gallas has been delighted with the impact his former Chelsea team-mate has made.
“I knew what he could do from my time with him at Chelsea,” Gallas said.
“He is doing a good job for us. He sits in front of the two centre-backs and he runs everywhere.
“His quality is really good. He can make crucial passes and I think he is one of the best midfielders in England.”
Sebastien Bassong started alongside Gallas in Russia but is likely to drop to the bench for this weekend’s game although he may not even make the match day squad after his blunder led to the goal which allowed Rubin to take all three points.
The former Newcastle defender admitted following the defeat that he is ready to leave White Hart Lane in January.
“We all know the situation at Spurs. If I get a chance to go I will go,” Bassong admitted.