In 2015 he was allegedly offered by Hoffenheim to a number of Premier League sides which included West Ham for a mere £5m before moving to Cologne. They are now said to value him at £33m but £25m is thought to be a more realistic valuation. He is contracted with the German side until June 2021.
Spurs, Southampton, West Brom and West Ham are all said to have scouted the striker in the past season and could be tempted to make a bid over the summer transfer window.
Modeste is said to be on a long list of strikers in Europe the Hammers would consider if they are not able to land their primary striker targets of Michy Batshuayi and Kelechi Iheanacho.