The Welshman is yet to begin contract extension talks and has caught the eye of a number of rival managers, particularly Antonio Conte.
Conte, who feels the Chelsea board's lack of investment has contributed to the side's fall from grace this season, will be keen to bolster his squad at Stamford Bridge after a disappointing season.
When asked by 'BT Sport' about a potential contract renewal, Ramsey said: "Nothing to comment on at the moment. I think they've been busy to tie up other contracts at the moment."
The 27-year-old has been at Arsenal since 2008, playing 319 games and netting 54 times. Now could be the time for a new adventure in his career.