Pogba's public declaration that he would be keen to leave for a "new challenge" has been compounded in recent days by the midfielder's agent, with Mino Raiola saying he was "in the process" of arranging a move for the World Cup victor.
"We're Man United and we don't need to sell our players", Solskjaer told a news conference at the WACA cricket ground.
"I'm positive. Of course with David I've said many times how lucky I am and happy we are to have him in goal".
"I'd like to say it's been an eagerly anticipated pre-season tour", Andy Mitten suggested from Manchester United's base in Australia, "but I've never known the mood to be so flat among supporters". Spoken to Rom, spoken to Rashy [Marcus Rashford], Jesse (Lingard) - I've spoken to all the players, more or less, over the summer.
"As far as I'm aware there have been no bids for any players".
"Paul, it looks like it's going to be a media".
"He's a great great professional and has a heart of gold". "Paul is a top bloke, a great professional".
Mino Raiola, Pogba's agent, poured more fuel on the fire yesterday by bizarrely claiming that United should have done more to support the player after he was criticised by fans for admitting he wanted a new challenge.
"People heard Solskjaer say that some of these players will not play for him again", explained Mitten, "and then they're seeing them play in pre-season and that doesn't instill confidence".
"There are fantastic players here, loads of players I know are gonna be successful at this club and we've signed two in Dan and Aaron, with their speed and hunger, with quality that will be part of that".
The English Premier League team plays its first match on Saturday against the A-League's Perth Glory. But Pogba is now exhausted of life in England and wants to play for a bigger club where he can win trophies on a regular basis and his agent has all but confirmed this when he spoke to reporters earlier this week.