The Sun says Reina was furious when Liverpool rejected a £20million bid from the Gunners in 2010.
But it looks like the Spaniard would be allowed to leave this time.
Moves have already been made to unite Reina with his fellow Spaniards and close pals Mikel Arteta and Santi Cazorla at the Emirates.
His wages, thought to be over £100,000 per week, were a stumbling block for the Gunners. But it now seems the London club is ready to commit big-money on top of a transfer fee of about £10m.
Reds boss Brendan Rodgers would be prepared to listen to offers for the keeper, provided he can secure a replacement.