The 34-year-old was most recently with Dundee after signing a short-term deal under John Brown in March and played eight games for the Tayside club in the SPL.
A former England under-21 cap, he is vastly experienced having previously played in the Premiership for Everton - where he worked under Walter Smith - and Stoke City.
Simonsen has also turned out for Tranmere Rovers, Sheffield United and Preston North End in a lengthy senior career dating back to his professional debut almost 16 years ago.
Gers have been interested in him for several weeks, with assistant manager Kenny McDowall confirming he was a player they were keen on during last month’s German training camp.
With Ally McCoist keen to put Scott Gallacher out on loan, he wants another senior player to come in and challenge Cammy Bell for a starting jersey.
The manager 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.
“Ideally, we’ll play Gall between now and the last week in August then we can look at maybe sending him to play somewhere else.
“Steve’s here for the rest of the week. He’ll train today, tomorrow and through to Friday then we’ll have a wee chat about things.”
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