The former Austria Under-21 international moved to Rugby Park from English Premier League side Watford on a one-year deal last summer, and has put in a string of impressive displays for the Ayrshire side.
In 19 games played in the Scottish Premiership this season, Bachmann has kept nine clean-sheets, the latest of which came in the weekend’s 5-0 thrashing of Hamilton.
The 24-year-old’s eye-catching performances have played a crucial role in Kilmarnock’s ascent towards the top of the Premiership table, with Steve Clarke’s men just six points behind second-placed Rangers.
And it seems Steven Gerrard has been impressed by what he’s seen from Killie’s shot-stopper this season.
Speaking to Austrian media outlets, via the Sun, Bachmann explained: “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.”
With Wes Foderingham now 28 and expected to move on in the summer, and first-choice Gers keeper Allan McGregor now 37, do you think Bachmann could be a clever signing by the Ibrox club?
Let us know in the comments section below…