Since moving to Old Trafford from Arsenal in January 2018, the Chilean struggled to find his best form and has spent the 2019-20 season on loan at San Siro.
Recent speculation has claimed that a permanent switch could be confirmed as soon as Thursday, which the Norwegian former striker has now confirmed.
"Yeah I believe so and I can confirm that," he told BT Sport after his side's 2-1 Europa League win over LASK.
Alexis has had a good time over there, he's a good player and we wish him all the best.
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The move was also confirmed by Inter CEO Beppe Marotta.
"It will be official tomorrow (Thursday) in the morning," Marotta told Sky Sports.
"The player is completely ours and we have a three-year contract with him. We think he can be a full member of our squad."
United were off the boil for large portions of the match against LASK and Solskjaer admitted that many of his heavily-rotated squad are lacking match practice.
"We learned the players need to play to keep that sharpness. Some of these lads haven't played for a while and it showed. We won, we gave a debut to a young lad, it's been a good night.
"It is that sharpness you lack when you don't play regularly, some haven't played since lockdown, for me it was a good exercise, it's job done, minutes under the belt and on to Copenhagen."
Goalscorer Jesse Lingard reacted angrily after being substituted and the England international admitted that he was keen to carry on playing.
"I was enjoying the game and I enjoy football matches. I felt like I could score more today but obviously it's the manager's decision and I stand by that."