Lukaku's incredible goalscoring record with his country has continued, leading many to feel his problems are simply with United.
If Lukaku does leave then the Red Devils will definitely miss his goals and so Solskjaer will have to replace him adequately.
Lukaku remains a "deadly" finisher according to his United team-mate Scott McTominay, who was on the receiving end of the Belgian's goalscoring for Scotland on Tuesday night.
The defender has since taken to social media to provide an update and it appears to be good news for Liverpool. Subscribe to our SMS sports service by texting "SPORTS" to 22840.
"Conte knows what I think about him".
The United striker, 26, scored only 12 times in the Premier League last season but took his worldwide record to 48 goals after scoring twice in Belgium's 3-0 win over Scotland, which kept them top of Group I in qualifying.
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"As for my future, I have already made a decision that I still can not communicate publicly out of respect for Manchester United with whom I have a contract".
"I have a contract and I have to respect my club".
Michael Bochel added: "Best Scotland away support I've seen in a wee while". 'I lost my place and haven't played much.
'I've had a hard season at club level, ' said Lukaku.
"Romelu is a fantastic character".
'I am going to enjoy my holidays with my family now.