The 23-year-old has made six appearances for United so far since joining for a month from Yeovil Town on New Year's Day and boss Brian Laws is hoping to extend Rose's stay at Glanford Park but there are other clubs interested in the left-back, including Keith Curle's Chester.
"I had a long chat with Michael and we will now wait for his response," explained Curle.
"He has a couple of other clubs who are interested in signing him, both of whom are in League One - but hopefully he will decide to come to us."
Iron manager Laws is confident though that the player will stay with United.
"Michael has come in and done a terrific job for us and we'd like to keep him a bit longer," said the Scunthorpe boss.
"We are going to talk to him this week. There is competition out there and a few clubs want to take him now but I am just hoping that Michael makes the decision to stay with us."