On Friday, the striker posted data that showed he had clocked the second quickest top speed during training in Perth behind only Diogo Dalot.
Sources have told ESPN FC that manager Ole Gunnar Solskjaer was left disappointed with Lukaku's decision to make confidential data public and ordered the Belgian to delete the post.
The 26-year-old, who has not travelled with the squad for the final friendly of the summer against AC Milan in Cardiff, is keen to leave Old Trafford for Juventus or Inter Milan.
He is yet to feature during preseason as he recovers from an ankle injury.
Negotiations are continuing with both Juventus and Inter Milan with Lukaku's future still up in the air. United value the former Everton man between £80 million and £90m and have rejected an offer of £54m from Inter.
Sources have told ESPN FC that talks with Juventus have been held up while Dybala decides whether he is willing to join United.