The Gunners have heavily been linked with the Portugal international in the last few transfer windows, while West Ham were close to signing the 25-year-old over the summer but to no avail.
It is believed that West Ham still remain keen on Carvalho while Arsene Wenger could be in the market to potentially replace Jack Wilshere, whose contract at the Emirates expires at the end of the season.
But Sporting Lisbon president Bruno de Carvalho has dismissed any rumours of a move for the midfielder happening this January.
Speaking to Portuguese newspaper Record, as reported by talkSPORT, de Carvalho said on the matter:
“Forget [it]. He is not transferable in January.
“If one day he leaves, wherever it is, we must ensure that the footballing aspect of the decision is not called into question.”