Fowler, 29, who made 23 appearances for the Brewers during the 2006/07 campaign, returned to the club last week on a loan deal until the end of the season.
He came on as a substitute in Albion's 3-3 draw at Accrington on Monday.
Asked if he would like to stay at the Pirelli Stadium, the player told BBC Radio Derby: "I would love to. The lads have welcomed me with open arms. The main thing is I want to keep playing football. It's something I love doing. I just want to play."
Fowler only joined League One leaders Doncaster from Fleetwood in January. Prior to his loan switch to Burton he was farmed out to Forest Green after making just four appearances for Rovers.