The Austrian keeper has shone since joining Kilmarnock on a season-long loan from Watford last year.
Bachmann, 24, kept yet another clean sheet on Saturday as Killie thrashed Hamilton 5-0 to go third in the Premiership - just six points behind Gers.
And Light Blues boss Steven Gerrard is understood to have targeted the Vienna-born ace, with No.1 Allan McGregor now 37 and Wes Foderingham a rumoured target of clubs down south.
Bachmann was sent off against Rangers in Killie’s 5-0 Scottish Cup defeat in February, but his red card was later overturned.
Bachmann told Austrian media: “Rangers have made contact with my English agents.
“Of course it is pleasing that people have taken notice of my performances. But for now I will focus exclusively on Kilmarnock.
“From June onwards I will be a Watford player once more, and I want to make my name in the Premier League.
“Right now I am only bothered about helping Kilmarnock achieve their objectives.”
German Bundesliga sides Stuttgart and Hannover have also been credited with interest in Bachmann.
The keeper previously played for Stoke, and had spells on loan to Wrexham, Ross County and Bury before joining Watford in 2017.
He is under contract with the Hornets until 2020.