Van Gaal's team has been criticised for lacking a competitive edge against the top sides in the Premier League this term - and they crashed out of the Champions League group stage.
United face the prospect of a third trophyless season since Sir Alex Ferguson retired if they exit the FA Cup against West Ham tonight (7pm).
They travel to the Hammers for their quarter-final replay knowing a last-four date with Everton at Wembley is the reward for victory.
"[Van Gaal] is my friend, I worked with him for a few years," Mourinho told Sky Sports.
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Alonso (left) played under Mourinho at the Bernabeu
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Alonso was already at Real Madrid when Mourinho arrived in 2010
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"I am always linked with jobs and in the summer I will have a job, but in this moment I can promise you I do not have a contract with any club.
"I am not in a position to turn (jobs) down, I am in a position to analyse. I am in a position to be open to any club or national team.
"I have to be honest, if possible I would prefer a club but I must analyse to see what is best for my career and to be back with everything I have.
"I would prefer [to be in England]. I love the country, I love the football here, my family is very stable and happy.