Robben will leave the five-time European champions when his contract expires in the summer and he will make his final appearance in their German Cup final clash against RB Leipzig this weekend.
According to Oddschecker, Leicester are now 2/1 favourites to sign the veteran winger – ahead of his former club PSV Einthoven.
However, Robben has not ruled out the possibility of hanging up his boots for good when he leaves the club.
“It is an option, but I don’t know whether it will happen,” Robben said.
“It is not an easy decision to make. If you decide that you are going to keep playing, you have to find a place where everything is just right, not just in terms of football but also for my family.”