United's home defeat by Norwich City last weekend, after which the Dutchman said he was "worried" about his position, was their third defeat in a row and they are without a win in six matches in all competitions.
Mourinho's sacking by Chelsea last week has increased speculation that Van Gaal could be replaced by the Portuguese three-times Premier League title winner.
"I do not want to get into a world of speculation, I personally have huge respect for Louis van Gaal," Wenger said at a news conference on Wednesday.
"What is going on there at the moment is disrespectful. This guy has worked for 30 years in football and delivered an unbelievable quality of work.
"Of course he deserves more time."
Wenger, whose team are second in the Premier League ahead of the busy Christmas programme, two points behind Leicester City, said Pep Guardiola's decision to announce that he will leave Bayern Munich at the end of the season added to the rumours.
Although he would welcome the Spaniard in England, should Guardiola end up in the Premier League.
"He is a top quality manager, not so much for what he has won already because Bayern won before he was there and (his former club) Barcelona are winning now, but because of his positive attitude towards the game and that he wants his teams to play in a positive manner, that I respect," he said.
"Personally I don't like that a manager comes out so early on their plans because it's not good for their own teams and increases speculations about the managers who are going through a difficult patch."
With Mourinho axed, Van Gaal under pressure and Manchester City's Manuel Pellegrini also coming under pressure, Wenger appeared serene on Wednesday, with his side bang in form and many predicting Arsenal will win the league.
Arsenal have won the most points in the top flight in the calendar year and beat Man City 2-1 on Monday.
"We lost our first game at home against West Ham and we were not absolutely sure that at Christmas we would be two points behind the leaders," Wenger said.
"But if you look back at 2015 we have been consistent, we've had a positive year and stabilised our defensive record and improved our record against the strong teams in the Premier League.
"So it looks like we are on the right train going the right way."
Arsenal are at Southampton on Saturday and host Bournemouth two days later.
(Reporting by Martyn Herman, editing by Pritha Sarkar)
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