The French striker only joined the Swans over the summer on a free transfer from Lyon, yet his future at the Liberty Stadium is in some doubt.
The experienced former Les Bleus international has played second fiddle to Wilfried Bony – who is wanted by Manchester City – which is rumoured to have left him frustrated.
Although Swansea are said to be desperate to keep the powerful marksman, Crystal Palace are already in the running for him – with a bid of £9.3m said to be on the table.
And now reports indicate that Arsenal have been contacted with a vie to offering Gomis an escape route.
The player himself is keen to test himself at the highest level, and would be available for the remainder of Arsenal’s Champions League campaign, which kicks off with a last-16 double header against Monaco.
Arsene Wenger is understood to be assessing loan exits for Joel Campbell and Yaya Sanogo, which could leave him short of attacking options.