The Southampton midfielder has expressed his desire to play in the Champions League should the opportunity arise and having pushed but failed to leave last summer, is expected to depart St Mary's in a £25m move this summer.
Arsenal have long been the favourites to sign the France international due to a combination of need in the midfield anchor role and Arsene Wenger's history of leaning towards compatriots in the transfer market.
However, Manchester United are understood to be lining up a rival bid with manager Louis van Gaal seeing 25-year-old Schneiderlin as a long-term replacement for the ageing Michael Carrick.
Michael Carrick will be 34 when next season starts (GETTY IMAGES)
Van Gaal got a close look at Schneiderlin in January when he put in a particularly eye-catching performance as Southampton picked up their first league victory over Manchester United at Old Trafford in 27 years.
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Schneiderlin has two years left on his contract, putting Southampton in a more difficult position if they try to resist attempts to sign the Frenchman again.
"I think my decision is made," the player said last week.
"The Champions League is my goal and if I leave Southampton it will be for a club in the Champions League."
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