Gunners boss Arsene Wenger has been chasing a new midfielder all summer and has been strongly linked with a move for Alonso, as Liverpool targeted Aston Villa's Gareth Barry.
Even though Liverpool missed out on Barry, reports claim they would have still sold Alonso to the Gunners had Wenger matched their valuation before the window closed.
Liverpool wanted more than the £14million on offer though, Wenger refused to go any higher and the deal subsequently collapsed.
Wenger was also said to be in the hunt for Sporting Lisbon midfielder Miguel Veloso but again could not push through a deal in time and will now go with what he has got until January.
Arsenal last week