The highly-rated 21-year-old impressed on-loan at the Blues earlier in the season, scoring six goals in 13 starts, before returning to the Premier League champions on January 1.
And Clark revealed that he is keen on borrowing the young forward again.
"I am still in conversation with David Moyes and his staff about Jesse," Clark told the Birmingham Mail
"That isn't completely dead."
The loan market is where Clark is looking to do further business this transfer window, and has his eye on several top flight targets.
"I am also having conversations with other clubs regarding some of the top young players to bring them in on loan," Clark added.
"I am trying to build a relationship with all these big clubs."