Van Gaal, currently in charge of Netherlands national team, has recently spoken openly about the possibility of taking over at White Hart Lane.
On February 9, Tottenham held talks with the Dutchman and was planning to once again discuss the possibility of offering him the job after the World Cup.
But Ginola, speaking at the time of those reports, said Sherwood should be given a chance to impress.
"You can always bring in the best managers or the best names around, but why don't you trust Tim Sherwood for another three, four, five years?" he told Goal. "I don't understand that. If he proves to everyone until the end of the season that he is capable of doing a good job at Spurs I don't know why he shouldn't have the job for another three years, at least, and work on the things he has been achieving so far."
The Portuguese spent 120 million euro on reinforcements, but he left the side in mid-December following a 5-0 humbling at the hands of Liverpool, and Ginola believes he got to the point where he was managing the club in fear.
"Villas-Boas didn't have any trust in his team going forward," he said. "So he was in a position where he was playing not to lose. He didn't want to play Adebayor, he didn't want to play anyone.
"He had one player in midfield making sure that they would not concede any goals and he was against the wall already. You can't manage a team when you are thinking that way."
The former France international believes Sherwood has shown himself capable of managing in the Premier League.
"Tim Sherwood has nothing to prove, in a way, because he's just come from the academy, he was working with the kids, he was watching the first team play but didn't have much to say about it, but as soon as he arrived he took Adebayor from the bench and put him up front, and with Villas-Boas, having spent 100 million euro on players in the summer, they realized that the results were not good enough."
Ginola believes that having former players involved in the running of the club, such as Sherwood and his assistants Les Ferdinand and Steffen Freund, is an ideal model for running a football club.
"I was in the dressing room after the Manchester City defeat and I saw Les Ferdinand, I saw Steffen Freund, I saw former players actually in the dressing room, and that was very interesting because I think in a club if you want to be successful in one way or another you need to have former players involved," he said. "The players know the club inside out, they make the right decisions, they do the right thing for the club and I think Tim, Les, Steffen, and all the guys involved in the staff do that. This is how they should look at the future."
Ginola also believes that Spurs should focus on what is best for them at this moment in time rather than trying to adhere to a tradition of open, attacking football.
"They can play good football, they play much better football [now]," he said. "They have [Nabil] Bentaleb in the middle, with flair as well, and they play with five players going forward. The strike force is much better, and I think it should always be like that, looking to score at least one more than the oppontent. This is how it should be.
"But I'm not really sure about thinking, 'Ok, it has been the case for 40 years [and you should play like that]', Why? Just because 40 years ago they were playing like that [it does not mean] today should be the same. You should just focus on what you are trying to achieve."