Solskjaer has impressed at Old Trafford since being named caretaker manager until the end of the season.
Nine wins from his first ten matches in all competitions has put the Norwegian in the frame to get the job on a permanent basis.
Tottenham boss Mauricio Pochettino is believed to be of interest to United as they look for a new manager after sacking Jose Mourinho.
Manchester United have impressed under Ole Gunnar Solskjaer, with players smiling again and playing more free-flowing football.
That’s familiar with the United style under Sir Alex Ferguson, who Solskjaer starred for.
And having impressed so far, Solskjaer has admitted he has spoken to executive vice-chairman Woodward about plans for the future.
“Well, every day I feel that I do help the club put my stamp on it, yes,” Solskjaer said.
“But decisions sometimes of players’ futures are not down to me either, it’s the players.
“Do they want to stay, move on? But we have a vision and picture of how we want to look in a few years and we have to think long term and also short term.
“I’ve got a picture of what this Manchester United team should look in a couple of years but I put my views to Ed and the club.”
Solskjaer has regularly stated his desire for the permanent job at Manchester United.
Nine wins and one draw from his first ten matches is almost the perfect job application.
But the Norwegian’s vision at the club hasn’t altered since coming in prior to Christmas.
He added: “Not really, because I’ve supported and followed Manchester United for many many years and I did have a clear view on what I thought my opinion would be.
“You get a different view on players but we’re not too far away from when I came.”
Solskjaer will look to get Manchester United into the Premier League top four when they travel to Fulham tomorrow (12.30pm).