Lukaku joined United from Everton in 2017 and has scored 28 Premier League goals across his two seasons at Old Trafford, but he has been a regular target for criticism from fans.
The Belgium international has received flak for his technical ability, control and perceived lack of ruthlessness in front of goal, finding himself usurped as first-choice striker by Marcus Rashford last term after Ole Gunnar Solskjaer replaced Jose Mourinho as manager.
Inter has made no secret of its interest in the 26-year-old, but a reported offer of €70 million ($113 million)) — comprising of a two-year loan and a €60 million ($96.8 million) obligation to buy — is said to have fallen significantly short of United's €83 million ($133.9 million)asking price.
With media reports suggesting Lukaku is more likely to stay at United than leave, the striker suggested news is imminent.
Speaking after United's 2-0 friendly win over Perth Glory, which Lukaku missed because of injury, he said: "You guys [the media] will know something next week."
Furthermore, Solskjaer expects Lukaku to feature in the Red Devils' next pre-season game against Leeds United on Wednesday, although the United manager was less definitive about whether the striker will still be at the club when the Premier League season starts.
"There's been so much speculation, but yes, he should be fit for Wednesday and he trained with the team yesterday [Friday] but it wasn't useful to risk him [against Perth Glory], to be fair," Solskjaer said.
"Can I see him staying? Let's see when the season starts. We've not had any bids we're considering.
"All my conversations I will keep confidential, that's my privilege and I can promise them that I won't tell them our discussions."
Paul Pogba is another big-name United player being linked with a move and he refused to offer any clarification over his future after Saturday's match.
When asked about his situation, Pogba said: "Who needs to talk? There's no need."
One person who has felt the need to talk is Pogba's agent Mino Raiola, who confirmed earlier this month the France international wants to leave United.