Malaysian businessman Tan has caused controversy by changing the club's kit from blue to red and sacking manager Malky Mackay after a series of disagreements.
But Tan claims to have ploughed more than £120million of his own money into the club and has already backed Solskjaer in the transfer market with the acquisitions of Magnus Wolff Eikrem and Mats Moller Daehli.
There were also three club-record signings during the summer and Solskjaer is confident Tan can help the Bluebirds become a top-10 side, and re-iterated he will have control over all football matters.
Solskjaer, whose side dropped into the relegation zone after defeat to West Ham last weekend, said: "The owner is a winner and he wants all of his businesses to be successful. Now he trusts me to make the football decisions.
"In the short term it is important that we stay in the Premier League, but then again he has reassured me that we are looking to strengthen if the right people are available.
"It is not like I have X amount of money. It is my job to find value for money and put it to him. He has been very open for discussion.
"It is a great football club and a top 10-place is the medium and long term aim, and who knows what can happen in the long, long term?"
On Saturday, Solskjaer takes his side to the Etihad Stadium to face a Manchester City side with 10 wins from 10 at home in the league and 99 goals scored in all competitions so far this season.
The Citizens remain in contention for a trophy quadruple.
Solskjaer famously helped Manchester United to the treble in 1999, scoring the winner against Bayern Munich in the Champions League final.
He feels City can achieve an astonishing feat, as long as they do not become fixated by the idea.
He said: "It's possible for them to win all four. They will go for it and want to win it.
"When you get into that position the thing is you don't talk too much about it at all, because you are in such a great frame of mind.
"You get into the rhythm of playing a game and performing, winning and playing and performing and winning.
"That was what we felt for the last five months of 1999. It was just game after game after game. We rotated and didn't have to make too many changes.
"We had won so many games and Peter Schmeichel's penalty save (in the FA Cup semi-final against Arsenal) was a key moment because Arsenal would have won the double.
"That's the margins in football."