Inter Milan want £44m for Manchester United target Ivan Perisic, Sky in Italy understands.
United are keen to bring the Croatia international to Old Trafford this summer and Sky in Italy understands they have had a new and improved bid turned down.
Sky sources revealed in May that United were in talks with Inter about the potential signing of Perisic and signalled their intent with an opening offer of £36m.
The Serie A club rejected that offer and Sky in Italy understands new manager Luciano Spalletti would be keen to keep Perisic at the San Siro if their £44m valuation is not met.
Perisic joined Inter from Wolfsburg in 2015 and has enjoyed a fine season in Serie A, contributing 10 goals and six assists.
He has three years remaining on his current contract at Inter.
United manager Jose Mourinho revealed last month that the club's executive vice-chairman Ed Woodward is in charge of negotiating deals this summer.
Mourinho told Sky Sports News HQ: "He [Woodward] knows since March, who I want, what I want, how much I want.
"He knows everything since March and now it's for him to work, because he will have holidays in August and I will be working."
Sky Sports News HQ also understands United are increasingly confident of signing Alvaro Morata and will continue negotiations with Real Madrid.
United are looking to bolster their forward line having allowed Zlatan Ibrahimovic, who is currently recovering from a cruciate knee ligament injury, to leave the club following the expiration of his contract.