But it is believed no concrete bid has been received from the Baggies for the Republic of Ireland international.
Albion boss Steve Clarke confirmed over the weekend that an offer had been rejected from relegated Blackburn for Cox.
Now Swansea are showing an interest in the former Swindon player who has struggled to win a regular first team place at the Hawthorns.
The 25-year-old has often been fourth choice striker in the face of competition from Shane Long, Peter Odemwingie and Marc-Antoine Fortune.
A source close to West Brom said there had been "several inquiries" for Cox.
Cox would prefer to stay in the Premier League if given the choice as it would also aid his hopes of becoming a regular starter for his country.
Clarke has also confirmed that Long, who joined Albion from Reading 12 months ago, is not for sale despite speculation linking him with a move back to his former club.
Source: PA
Source: PA