Reports over the weekend suggested that United had switched targets to Wigan's Ali Al-Habsi but there will still be plenty of interest in Begovic ahead of the summer.
Sir Alex Ferguson has given his backing to David de Gea and believes he will be a top goalkeeper for years to come but he wants quality cover and sees Begovic as the ideal signing.
Stoke boss Tony Pulis has not ruled out Begovic staying even though Jack Butland has been brought in from Birmingham.
There have been suggestions that Butland could be loaned out next season to get more experience and, if that is the case, then Begovic will be needed at the Britannia Stadium.
However, their resolve will be tested as United look to sell Lindegaard to help fund a £15million move for Begovic.