HITC Sport understands West Brom and Swansea are eyeing the Senegal star.
Konate has been a target for a number of Premier League clubs over the last couple of years after impressing for club and country.
The Senegal international scored 22 goals in 33 games for Sion last season in all competitions and he has netted seven times in 16 appearances for his country.
FC Sion's Moussa Konate celebrates after scoring
Konate has impressed at Sion since joining the club from Russian side Kuban Krasnodar two seasons ago and the Senegalese international is considered one of the most promising young strikers in Europe.
West Brom and Swansea have expressed an interest in Konate as they look to strengthen their attacking options before the transfer window closes.
Senegal's Moussa Konate (L) in action with UAE's Esmaeel Khamis
West Brom are in desperate need to bring in a new striker after seeing a deal for Konate's Senegal team-mate Diafra Sakho fall through over concerns with the West Ham forward's fitness.
Swansea are still in the market for striking reinforcements despite the recent arrivals of Atletico Madrid striker Borja Baston and Sevilla front-man Fernando Llorente, having seen Andre Ayew, Bafetimbi Gomis and Alberto Paloschi all leave the Liberty Stadium this summer.