Burke, a Scottish international, spent the majority of last season on loan at Millwall as they threatened to gatecrash the Championship play-off places.
With another year remaining on his United contract, Burke is expected to be made available for a move elsewhere this summer - and Rowett would be keen on a reunion if a deal can be done.
“Oli had a good time here last season,” Rowett told News at Den.
“If Sheffield United decide that he’s not part of their plans, then of course he’s the type of player that we’d like to bring back in.
“It’s the level of player that we’d like to try and bring in this summer, and we’ll work incredibly hard to make that happen.
“It’s easy to look and say that we haven’t done much yet, but there’s been a lot of work behind the scenes that I believe will come to fruition in the next week.”
Burke, who joined United in a swap deal involving Callum Robinson while United were still a Premier League club, has scored once in the league for the Blades and doubled that tally last season for Millwall, from 10 Championship starts.
Rowett confirmed earlier this week that his side have permanent bids in for a couple of players, which he expects would eclipse their record signing - the £1.5m paid to United for Ryan Leonard.