Both clubs are also keen to move the match back a day from Sunday, 4 April to a lunchtime or early evening kick-off on the Saturday - Grand National Day.
It would allow them extra time to prepare for possible Champions League action the following week.
If the FA agreed to switch the game to Saturday, 3 April, Villa Park would be ruled out because Aston Villa have a home Premiership game against Manchester City scheduled for that day.
However, United are keen to keep the game in Birmingham because they have a fine record at the Midlands ground.
It was the scene of United's dramatic FA Cup semi-final victory over Arsenal in 1999, when Ryan Giggs scored one of the greatest ever Cup goals.
After seeing the draw, United boss Sir Alex Ferguson commented: "A semi-final at Villa Park - that's a good venue for us."
Manchester United appeared to be showing no sign of changing their minds today. A club spokesman said: "We are happy to play at Villa Park."
Arsenal and United face each other in the Premiership at Highbury the weekend before the Cup tie, so there are likely to be mass withdrawals from the England side for the friendly in Sweden sandwiched between the two highprofile matches.
It was reported today that the FA are keen to set up a meeting between England coach Sven-Goran Eriksson, Arsene Wenger and Ferguson to discuss a compromise that will suit all parties.
At the very least, the Arsenal and United bosses will expect preferential treatment for their players in Sweden.
