Both Aston Villa and Birmingham City have offered deals to the Chelsea defender, who's contract expires at the end of this month.
West Brom are also keen on the former England captain and are confident they can offer more money, although Terry may avoid a Premier League move to limit his chances of playing Chelsea next season.
Villa have put forward a lucrative deal which would see the 36-year-old earn around £60,000-a-week and receive a significant bonus should Villa win promotion - and are the bookies favourites in the race for his signature.
Steve Bruce was pictured alongside Terry earlier this month during a golfing trip to Portugal, and the Englishman has been training at Chelsea following his return to the country.
Swansea and Bournemouth are also rumoured to be interested in the Chelsea legend, who has four Premier League titles to his name.
Meanwhile, Villa face a renewed challenge for Sam Johnstone. Middlesbrough are interested in the goalkeeper and are reportedly in talks with Manchester United over a potential £2.5million deal.