The defender joined the Blues from Burnley last summer, becoming one of their key players in a disappointing campaign that ended in relegation to the Championship.
As a result, O'Shea has been linked with a move away from Portman Road. Wolves and Leeds United are both reportedly interested, as have former club Burnley, but the 26-year-old has stressed that his priority is to get Town back into the top flight.
“I'm fully committed to Ipswich at the moment," he said via the Irish Mirror. "I've got another four years there and I want to get the club back into the Premier League.
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“I'm ambitious as a player and obviously I want to be playing in the Premier League but I know it's not as easy as that. Whatever happens in football it happens for a reason. You have a journey and you've got to stick to that sometimes.
“I feel like I'm well capable of playing in the Premier League and I've got to get myself back there now. I spoke to the gaffer at Ipswich and that's the task he's set me - to carry on those standards of a Premier League player and still owe it to myself to be like that.
“It’s really hard when you come off the back of relegation but I'm happy with how I played. I’ve grown into a leader and I play better when I have that responsibility.”