Rovers boss Gary Bowyer has confirmed that the club will monitor the 28-year-old over the next week before deciding whether to offer the forward a full-time contract.
He told the Lancashire Telegraph: "We're just having a look at him. I know one or two clubs are also looking at him so it's a chance to assess him in training.
"He looks fit and he'll continue to train with us for a couple more days and maybe next week as well. Then we'll see how it goes."
Simpson has also previously played for Cambridge United, Coventry City and Huddersfield Town.