Ribery has just signed a new deal with the Bavarians to keep him at the Bundesliga giants until the end of the 2017-2018 season but Robben will fall out of contract in the summer of 2017.
There is still time to sort out new terms but the Netherlands international will be free to talk to clubs in January if he has not penned an extension with Bayern.
Chairman Karl-Heinz Rummenigge says Bayern chiefs will hold renewal talks with Robben after Christmas and Ribery hopes that they are successful.
“Arjen is a very important player for Bayern,” he told Goal. “We need players like Arjen. Players with a lot of experience and a big name. That is part of Bayern.”
Gareth Bale could leave Real Madrid this summer despite proving to be the match-winner during Saturday's Champions League final.
Brighton are stepping up their recruitment drive this summer with Reading defender Liam Moore next on their list of targets.
Everton are in the hunt to sign Chelsea striker Michy Batshuayi but he will not make a decision until after the World Cup.
Manchester City goalkeeper Joe Hart has emerged as a shock transfer target for arch rivals Manchester United this summer.
Chelsea are showing an interest in Napoli full-back Elseid Hysaj, who could join Maurizio Sarri at Stamford Bridge, reports claim.
Arsenal are reported to be locked in talks with Switzerland right-back Stephan Lichtsteiner, who is set to leave Juventus.
Gareth Bale has suggested he could be on the move following his Champions League heroics, with Manchester United in the hunt.