The 22-year-old attacking midfield has been a standout performer for the Welsh side this season, scoring six goals in just 11 Premier League appearances.
||Gylfi Sigurdsson is 7/1 with Paddy Power to score the first goal when Swansea play Newcastle on Saturday.
Brian McDermott managed the Iceland international at Reading and believes he has the quality to play for Wenger's side.
“I spoke to Arsene about him and you could not tell me he could not play for Arsenal,” he said.
Although Sigurdsson hasn't yet proved himself at a big club, he has just been named as the Premier League's Player of the Month for March. With the Gunners in a strong position to secure Champions League football next season, a move to north London would be an exciting proposition for the youngster.
Cesc Fabregas and Samir Nasri's departures last summer mean there is space in a side that desperately needs fresh talent in order to try and end a seven-year trophy drought.