After recently signing shot-stopper Jose Moreira from Benfica, the promoted Swans have stated their intention to further strengthen their options between the posts following Dorus de Vries' exit to Wolves.
But Swans chairman Huw Jenkins has already confirmed that Fulham keeper David Stockdale is unlikely to join the Welsh side, and Rodgers has now also ruled out Green.
"We haven't spoken to Robert," he told Sky Sports News. "He's obviously a fantastic keeper but he wasn't one that we've spoken about."
Rodgers added of Stockdale: "Obviously David Stockdale is very keen to come but he's a signed player with Fulham and they're looking to get him loan experience. Maybe that's out of our hands."
The Swans boss also admits he has called time on his interest in Gudjohnsen, with the former Chelsea striker likely to go to West Ham.
He said: "Eidur won't be coming. I spoke to him again last night and I think he'll probably end up going to London to be at West Ham."
Swansea have made three additions to their squad so far this summer, and Rodgers is keen to sign a few more fresh faces ahead of their debut season in the top-flight.
"I feel I only need to add three or four to give us an opportunity to stay in what is a fantastic league," he said.
"The players we have, I believe, will show up very well.
"If I can support them by bringing in three or four more I think we can surprise a few people this year."