He told BBC Radio Stoke: "The manager has known me a long time and he knows it would benefit me hugely to be playing regular football.
"Whether that comes in the form of a loan move or a permanent move I don't know, but I wouldn't rule it out."
Simonsen, who has played 187 games for Stoke since signing on a free transfer from Everton in July 2004, spent the final seven weeks of the season on loan at Championship side Sheffield United.
The former Tranmere goalkeeper was displaced as the Potters' number one by Sorensen following Stoke's promotion to the Premier League in 2008 and fell further down the pecking order when Begovic joined from Portsmouth for £3.25m in February.
Simonsen has played just eight games in the top flight for Stoke, three as a substitute.
The former England Under-21 international added that despite his affinity for the club, remaining the third-choice goalkeeper at Stoke is not something that appeals to him.
"You're never entirely happy being second-choice goalkeeper," said Simonsen. "It's slightly different because you're always involved in the squad every week.
If the chance comes to move on, I will certainly think about it and maybe it will happen
Stoke City goalkeeper, Steve Simonsen
"Although I wasn't frozen out cold, the manager wanted me to stay amongst the squad, but it's tough watching the games when you're not involved.
"It's always on the cards that I may well move on, depending on what comes in. I've already been on loan to Sheffield United, which was thoroughly enjoyable.
"Everyone knows I have a huge passion for Stoke City and that will never die. I've been here for so long, I've seen the low points of the club and the highest points.
"But in football, you can't hang around somewhere just because you love the place. You've got to think about your own career.
"If the chance comes to move on, I will certainly think about it and maybe it will happen."
Source: BBC Sport
Source: BBC Sport