The Welsh midfielder is out of contract in the summer, as he could not agree on a new deal with the club.
Speculation had suggested he would move on a cut price deal in the winter transfer window. But he has put those rumours to bed.
However, Ramsey is quoted by Sky Sports as saying: "I am contracted to Arsenal and I am going to do my best now this season to try and achieve something special.
"Everything has been going great with the club.
"We thought we were in a position where we had agreed a deal but that's no longer the case.
"So I just have to carry on playing my football and do my best for Arsenal this season, and I'll leave the rest with the club now."