Manchester United want to complete the signing of Southampton midfielder Morgan Schneiderlin before flying to California next Monday.
Manager Louis van Gaal is keen to have the Frenchman among his squad for the pre-season tour of the US, where United will play four matches in two weeks.
Ronald Koeman is also said to be keen on getting a deal done as quickly as possible, so he can find a suitable replacement sooner rather than later; Koeman is understanding of Schneiderlin's desire to make a "big move".
Memphis Depay's first training session
United have already had one offer of £20million - described as "not serious" by the Southampton manager - rejected by the South Coast club. Southampton value the 25-year-old at around £30m but United remain hopeful that he could be bought for £25m.
Both clubs realise that time is now pressing, and a failure to push through the move would leave them both playing catch-up when the Premier League season starts on 8 August.
"Everybody knows the situation of Morgan and if you can get a big move I can understand it,' Koeman said on Monday.
"If there is any business then I hope it will be soon because it is best for the player, best for us and we have to think about ourselves if we sell the player.
"I had a lot of meetings with Morgan - I already had a meeting last week with Morgan - and it is important for the player to do a good pre-season and we will see what happens in the next few days."
It is reported that United's offer for Schneiderlin was in the region of £20million. Asked what fee would persuade Southampton to sell, Koeman added: "I don't talk about money, about numbers. It is not my business. It is up to the club."
Additional reporting by PAReuse content