Agent Mino Raiola compounded matters by talking about how he is working to get his client a move, but Solskjaer says he would still consider the midfielder for a leadership role this season.
Lukaku is a target for Inter Milan but United have told the Serie A side they will need to pay more than £79m to sign the 26-year-old Belgium worldwide, increasing the prospect of him staying at Old Trafford.
The Wales global operated down each flank at times, and showed bursts of his lightning pace, and speaking after the game the United boss tipped him to provide many exciting moments with the Red Devils.
Though a bid was not made, United reportedly reached out to the Serie A club as to the defender's availability.
They then face Leeds United before travelling to Singapore for the International Champions Cup meeting with Inter.
The Norwegian was believed to have held talks with the 26-year-old earlier this week in an attempt to persuade the attacker to spend at least one more season with the Premier League club. "I think Youngy also showed that he could go inside and play as that third central midfield player and he was playing me in quite a lot".