Mourinho was sacked by Chelsea last week, just seven months after lifting the Premier League trophy with the Blues, following a run that left champions Chelsea one point above the relegation zone.
The three-times Premier League winner issued a statement insisting he will not be taking a sabbatical.
Pressure has been mounting on United's Dutch manager with a six-game winless streak that saw the club bow out of the Champions League in the group stages and out of the top-four in the Premier League.
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Mourinho, who worked with Van Gaal during a successful spell at Barcelona, was previously linked to the Old Trafford job when former United boss Alex Ferguson retired in 2013.
Van Gaal is scheduled for a routine press conference on Wednesday evening ahead of Saturday's trip to Stoke City. Two days later the club will host champions Chelsea.
(Reporting by Chris Peters in Bengaluru; editing by Sudipto Ganguly)
