It is likely that Wimmer is being signed as a contingency plan for if - and potentially when - Evans departs for the Etihad stadium, and also comes after Pulis ended his own interest in prising Middlesbrough captain Ben Gibson away from the north east.
West Brom and Spurs appear to have agreed a fee of £15 million for the 24-year-old defender.
It is said that negotiations between Spurs and West Brom are at an "advanced stage" and a deal could be done in time for Wimmer to make his debut for the Midlands club's trip to Burnley on Saturday.
Irish Businesses Welcome UK Position On Brexit Customs Checks
The two issues are intrinsically linked, with the dynamic at the border dependent on the shape of future customs relations between the United Kingdom and EU.
A move for Wimmer will increase speculation Baggies skipper Jonny Evans is set for a big money move to Manchester City.
The 24-year-old, who is an Austrian worldwide, has been a long-term target for Tony Pulis with the boss hopeful of completing a deal for the centre-back in the coming days.
Sky sources understand no official bid has yet been made, but Albion have approached Spurs to ask whether they are prepared to sell.