The La Liga club are powerless to stop Laporte joining City if the Premier League leaders activate the centre back’s £57m release clause, and they are searching for alternative players who have a Basque heritage.
Monreal was born in Pamplona, within the borders of the Basque region, and played for Osasuna before making the switch to the Gunners in 2013.
Bilbao will be cash rich after Laporte’s sale, and they could make a bid for the Arsenal star with the player heading into the last 18 months of his contract at the Emirates.
However, Monreal is not the only player that the La Liga side are looking at. Real Sociedad’s Inigo Martinez has a release clause of €32m (£28m) which they could look to trigger, but Bilbao would see that as a far more costly outlay.