Chantome is set to become a free agent in the summer transfer window, as his current contract with French club Bordeaux runs out at the end of the month.
The identity of the two Premier League clubs that the 28-year-old midfielder is (reportedly) in advanced talks with has not been disclosed, though.
The France international has been linked with a number of clubs in the Premier League.
The former Paris Saint-Germain midfielder scored one goal and created 12 chances in 25 Ligue 1 appearances for Bordeaux last season.
Chantome had a pass accuracy of 88% and a shot accuracy of 29%, and won 92 headers, 16 dribbles and 51 tackles.
During the 2014-15 campaign, the Frenchman created 13 chances in 13 Ligue 1 matches for Bordeaux.
Bordeaux finished 11th in Ligue 1 during the 2015-16 season.