The Premier League side had an offer accepted for the Ivory Coast international, but the 49-year-old coach revealed that they had been unable to agree a deal with the player.
Kalou joined the Ligue 1 side at the start of last season from Chelsea, and the West Brom boss admitted luring the 28-year-old back to England had been tough.
"I don't think anybody has been able to persuade Salomon to come out of France," he told The Birmingham Mail. "The closer you get to the start of our season, the closer you get to the start of the French season.
"It doesn't look as if that one will happen, but that's normal in any transfer season.
"It's not just us who couldn't persuade him. A few clubs wanted him."
However, Clarke did reveal that he was still looking to bring in new faces ahead of the new season, and talks are ongoing with Manchester City over Scott Sinclair.
"We've made an inquiry to Manchester City," he added. "There are discussions between the two clubs but beyond that there is nothing to report.
"It would be nice to think we can get one in before Saturday. If we can get two in, it would be great. If I can get three, I would be delighted."