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.
Turner Scores UEFA Deal, Plans OTT Sports Platform
Numerous most important Champions League games, including the semifinals and final, will still be broadcast on cable television. Turner is to launch the yet-to-be-named service before the start of the next UEFA Champions League season in September 2018.
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.