Hudson has only played two Capital One Cup games this season.
The defender hopes to impress Solskjaer if he plays in the FA Cup third round tie at Newcastle United on Saturday.
"It's fresh eyes looking on the team and hopefully for myself, I'll look to impress and get myself into the team," said Hudson.
He has been kept out of the Premier League side by Steven Caulker and Ben Turner. It's been a frustrating time for Hudson but maybe he can get a chance under Solskjaer.
"To be honest the boys that have played have done well," said Hudson.
"I spoke to Malky quite a bit. We got on well. He was honest and just said, 'you have to wait for your chance', which I've done.
"I wish him all the best and have nothing bad to say about him at all. Obviously we are into a new chapter now."
Hudson is looking forward to showing the Norwegian what he can offer.
"He knows a lot about the game and it's really exciting times," said Hudson.
"He wants to play entertaining football, which I'm looking forward to being a part of.
"I know what I can add to the team but it's down to me to show the manager."