The 28-year-old enjoyed an impressive debut season with les Dogues, netting 14 goals in 28 Ligue 1 appearances after joining on a free transfer following his release by Chelsea.
But despite being trailed by several Premier League sides, including West Ham and West Brom, Kalou is eager to stay in France and work under recently appointed Lille boss Rene Girard.
"Rene Girard is a coach who can help me progress," the Ivorian told Voix du Nord. "Under these conditions, I do not see why I should go for something elsewhere."
The Hammers had been confident of completing a €4 million deal as Allardyce sought to bolster his attacking options, while the Baggies were interested in reuniting the forward with Nicolas Anelka at the Hawthorns.