Solskjaer has won his opening three matches in convincing fashion, scoring a total of 12 goals against Cardiff, Huddersfield and Bournemouth, and there are calls for the 45-year-old to be hired on a permanent basis.
While Shaw struggled to fully win over Mourinho during the Portugueses tenure, Uniteds left-back appears to be thriving under Solskjaer and has played every of the Norwegians impressive start.
The England international insists there is now a great buzz around United as the club prepares to take on Newcastle at St James Park on Wednesday night.
Thanks Jose for what he did for the club and for me as a person and a player, Shaw told Sky Sports.
Ole has a completely different style to his way and we are adapting to that and enjoying it and thats the main thing.
Theres a great buzz around the place with Ole coming back in, theres a lot of good things to look forward to.
Ole is a really positive and friendly guy and knows this club really well as he was here for many years and he knows what the club needs.
He is here for six months and its a massive thing for him to do an amazing job and that would be great for him.
We all back him and want the best for him as much as he wants the best for us. We all have to work together and keep doing the right things and keep smiles on faces and keep winning matches.
Shaw, who signed a new long-term deal at Old Trafford back in October, stresses that United are determined to work their way up the table after a dismal start to the season.
I signed a new contract and I want to be playing every game and trying to help the team as much as possible, he said.
Hopefully I keep playing games and keep myself in the team.
I havent had many injuries recently so thats good. I need to stay fit and keep helping the team and maybe win a cup this season.
“We are not where we want to be and not where we should be, so we have a very important second half of the season.
Our aim is to get back into the top four because United without Champions League isnt good. Thats where we want to be and what we are fighting for.