Manchester United have rejected a £54m bid from Internazionale for Romelu Lukaku and informed the Italian club it will need a significantly higher offer to succeed in luring the player away from Old Trafford.

Lukaku missed the pre-season friendly between the two clubs in Singapore on Saturday, after complaining of an ankle injury and was seen talking to Inter officials on the pitch after a 1-0 victory for Ole Gunnar Solskjær’s team, courtesy of a second-half winner from Mason Greenwood.

Inter are now contemplating lodging another offer and Antonio Conte, who confirmed his interest in the player on Friday, made it clear again after the match that he was still keen to take the Belgian striker to Serie A.

“I think that I have answered yesterday about Lukaku,” the Inter head coach said. “I think that it’s not right to speak about the player that in this moment is a United player. For this reason I think we must show great respect for the club and at the same time also for the player and also for my players.

“As I said yesterday, Lukaku is a player I like. I like him because I consider him a player that could improve our team. In one side there is my hope, my will. In the other side we’ll see what we find with the club.”

Two years since moving to Old Trafford Lukaku is keen for the transfer to happen but United rejected the bid out of hand because it fell considerably short of their valuation for the former Everton player.

Asked about Inter’s bid – and United’s ongoing interest in the Leicester defender Harry Maguire – Solskjær said: “Of course you want to have your team settled as early as possible. Whoever’s available, we work with them .... and let’s see on August 8 or 9 who’s here and who’s not.”

Lukaku has yet to feature for United in pre-season and that appears to be frustrating his manager. “If you’re a player and you don’t manage to train for a week – and he’s missed three games now – of course I think he’ll be concerned,” Solskjær said. “He’s working to get back on the pitch and let’s see how long that takes.”

Of Greenwood’s performance, Solskjær added: “The kid’s only 17 and he’s learning every day training with these boys. He reminds me a little bit about the Giggsy [Ryan Giggs] story, that you can’t really send him on loan. For me he’s ready to be in this squad.”

Solskjær was less impressed that Ashley Young was booed and jeered by United’s fans during the match. “I think Ashley is a top professional,” the manager said. “He always gives absolutely everything and his delivery ended up with a goal. Of course, we want fans to support our players. Ash has been a very loyal servant to this club for many, many years and he’ll keep on performing when he plays. We’ll have a chat with him but I don’t think he’ll get affected.”