Simpson is available as a free agent, with the former Cambridge United, Coventry City and Huddersfield Town forward having been released by Oldham Athletic at the end of last season.
Blackburn boss Gary Bowyer is prepared to give the 28-year-old an opportunity to prove his worth, with Rovers always on the lookout for possible additions to their ranks.
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."
Bowyer has also expressed a desire to put a deal in place which will keep promising midfielder Cairney at Ewood Park long-term, with the 22-year-old due back at Hull City in the New Year.
He added: "He's a very good, technical player and we were fortunate we were able to get him when we did.
"I think everyone would agree that they would want Tom Cairney to stay at our football club not just until May, but for a long time.
"That's something we'll be working toward, that's for sure."