The former France international right-back was released by Manchester City this summer and is still looking to get fixed up with a new club.
It’s understood his camp have also been approached by former champions Leicester City and Premier League new boys Brighton & Hove Albion, asking after his present situation.
Sagna’s talented footballing offspring, Elias, however, is still believed to be training with City’s youth academy and the family remain happy living in the Cheshire area.
That could now be the clincher for the Baggies, with Sagna’s commute to the Hawthorns only an hour or so away and current Albion skipper Jonny Evans already making a similar journey.
Sagna, 34, has had offers from abroad but likes living in England and is realistic with his own pay demands of around £50k per week.
The former Arsenal man is a model pro and has kept himself in tip-top shape this summer, which has further attracted Baggies boss Tony Pulis.