Middlesbrough are the latest club reported to have registered an interest in Dobbie, with Blackpool and Birmingham previously linked with the midfielder.
Dobbie was a key figure in Swansea's promotion success but has been left out of their matchday squads recently and has not played at all in 2012.
But Rodgers has insisted he cannot afford to let the 29-year-old leave.
He said: "I have got empathy for Stephen. But I have to protect the club so none of the senior players will be going out.
"I have spoken to Stephen to explain the situation and I'm sure he has been frustrated not to make the squads.
"But the players are well paid, so it's just unlucky for them and he has to get on with it.
"I know Stephen wants to play games.
"The great thing about him is that he is not driven by money - he is purely driven by playing football.
"But ultimately I have got to think about what happens at Swansea City.
"Look at what happened last week - all of a sudden we lost two players in a couple of days to injury in Joe Allen and Kemy Agustien.
"We could well lose more players over a longer period and, when that happens, I need players at Swansea who I can call on."