The 34-year-old shot-stopper headed for Scotland in March when penning a short-term deal with Dundee.
The former Everton, Stoke City and Sheffield United man impressed during his time at Dens Park and now has several options to consider after becoming a free agent.
Simonsen admits to having enjoyed his time in the SPL and would be open to prolonging his career with either the Saints or Dons.
He said in the Daily Record: "There's now interest from St Mirren as well.
"I loved my time in the SPL and would like to play there again.
"Scottish football opened my eyes and I would have no hesitation going back there."