The 27-year-old played every minute of Poland's Euro 2020 campaign, helping his country reach the last-16 stage of the competition.
The stopper made 26 appearances for the Hornets during the 2020-21 campaign, meanwhile, and finished the season as the club's number one.
According to The Sun, the Gunners have also shown an interest in Bachmann, but Watford have made it clear that the former Stoke City youngster is not available this summer.
Mikel Arteta's side could now allegedly switch their attention back to Ramsdale, but Sheffield United are thought to want in excess of £30m for the Englishman. body check tags ::