His ninth goal of the season in Saturday's 1-0 win over Sheffield United took Sunderland a step nearer the Championship's automatic promotion places.
The 32-year-old is out of contract in the summer and there's been no offer of a new deal, but he still has the desire to test himself at the highest level.
"I would love to have a go in the Premiership to see if I can still do it," said Stewart.
"It is one of my ambitions to play in the top flight again.
"I'll give my best here this season and see what happens.
"There has been nothing said at all about contracts, but that's not the most important thing here.
"The important thing is to try to get this club back into the Premiership.
"I enjoyed my time in the Premiership at Ipswich. It was a bit harder after I came here.
"Reidy (Peter Reid) signed me here, but got the sack within a month. Howard Wilkinson arrived and kept playing me, but on the right wing. He must have wanted to utilise my pace!
"But things have gone well the last couple of seasons. I don't think I'm as sharp or as quick as I was, but there are other parts of my game that have got better and it would be great to test myself against the best again."
Stewart's strike partner Stephen Elliott set up the winning goal against the Blades to opening up some daylight between Sunderland in third and the chasing pack.
"Sheffield were two points behind us a couple of weeks ago, but now they're eight points behind and Reading are six points back in fourth, so we have a buffer," said Stewart.
"We would like to be up there on top of the league. At the moment, we're the third-best team and we're chasing.
"We want to avoid the play-offs if we can, so we have to keep this sort of form going.
"I'm pleased to have scored on Saturday, especially with it being the winner. With Wigan and Ipswich only drawing, it was a good day all round for us.
"We have difficult away games coming now against Everton in the FA Cup and then Wolves in the league, but the telling month will be April - I'm still sure of that."
The Black Cats have to play Ipswich Town, Wigan Athletic and West Ham United away from home in April as well as hosting Reading.