The 34-year-old played eight games for Dundee last season but was not offered a new deal in the wake of their relegation from the SPL at the end of the campaign.
Rangers have started the season with youngster Scott Gallacher in goal, but they are looking at Simonsen with a view to the end of their transfer embargo at the start of September, when he would provide another summer signing Cammy Bell with competition.
Bell is yet to figure in a competitive game for Rangers, who are unable to field all of their new players in matches because of the embargo, but when he does become available Gallacher is expected to be sent out on loan.
McCoist said: "In an ideal world, we'd put Gall out on loan so that he's playing every week and we could bring another goalkeeper in to compete for the number one spot.
"Steve has come in and we're very thankful to him for doing that. We can have a look at him and he can have a look at our place as well. We'll see where that takes us.
"Nothing's set in stone at the moment. I've not seen him in training yet but I saw him in the gymnasium just there and he looks like he has been looking after himself.
"I don't think his fitness will be a problem and we've obviously spoken to one or two people about him who recommended him highly.
"Steve has been training here and there and I think he has had one or two other offers from other places which he has had to weigh up. The bottom line is there's no immediate rush for us to do anything because of the situation we're in at the moment."