Solskjaer held a press conference this morning to preview Manchester United’s trip to Wolves on Monday night.
The manager was quizzed on the Sanchez’s situation after reports emerged the Chilean had been made to train with the reserves.
Solskjaer unconvincingly attempted to offer the forward a lifeline back into his plans for the season.
But Mills felt the Norwegian did not do enough to put the situation to bed.
“I thought it was a really strange interview from Ole Gunnar Solskjaer,” Mills told Sky Sports.
“He didn’t conduct that, he wasn’t the authority was he? He wasn’t in command of that interview.
“He almost looked a little bit sheepish at times the way he answered some of those questions.
“It is like he wasn’t sure what was going on.
“He was trying to do his best for Alexis Sanchez saying ‘He is a great professional. He comes in and works hard. He has not been put in the reserves, he has been training with the first team’.
“I think a lot of managers would have come out and said this is the situation, he is not quite fit, he is nearly there – done and dusted.
“I think sometimes Ole is a little bit too honest ad open with the press. All of a sudden now I think that has cast more doubt on Alexis Sanchez’s future.”
Sanchez could leave Old Trafford over the next few weeks but his enormous wages would likely put off potential suitors.
“Alexis is such a professional and he comes in working every single day really hard,” Solskjaer said.
“And he wants to be a part of this and it’s these stories he’s again that he’s been put in the reserves, of course he hasn’t. He’s a part of our squad and a very, very good player.
“He’s had three weeks now, he’s a few weeks behind the rest but he’s close to being part of it. We don’t have the biggest forward line in numbers, so Alexis might end up playing a lot more games than you expect, because we expect him to come good at this club, he’s quality.
“We’ve had a behind closed doors game, and he’s training, he’s doing a little bit of extras, he’ll be gradually integrated into more and more playing time, but we’ll have more behind closed doors games.
“With one game a week now, it’s hard to keep players ticking, so we’re arranging a few of them.”