Saints boss Ronald Koeman confirmed last week there had been no further bids for the French midfielder since United had an initial approach rejected last month.
Koeman, whose team are in Austria this weekend for a pre-season four-team tournament at the Red Bull Arena in Salzburg, insisted last week that he wants Schneiderlin’s future sorted as soon as possible after his player missed the first day of training.
With the news that Louis van Gaal’s United had agreed a fee with Bayern Munich for Germany midfielder Schweinsteiger some may think United’s interest in another midfielder would have cooled.
However, on Saturday afternoon Sky sources believe Schneiderlin is still firmly on United’s radar.
Koeman recently played down reports that Schneiderlin had already agreed an exit strategy, saying the midfielder missed pre-season training because of illness after consulting a doctor and would make the trip to Austria.
After Southampton’s 5-4 defeat by Red Bull Leipzig, Schneiderlin was not in the team to face Valencia in their second tournament match on Saturday afternoon.