The 20-year-old has made six appearances for Hatters since joining on deadline day from League Two Gillingham.
He finally earned his first start in the 2-1 win at Tamworth on Tuesday night and kept his place for Saturday’s 3-1 triumph over Southport too.
Essam said: “It looks like it’s going to be extended, which I’m pleased about.
Essam became noticeably more imposing during the game on Saturday, especially his aerial dominance of the Sandgrounders frontline, a fact that wasn’t lost on Town boss Paul Buckle, who is hoping an extension can be agreed.
He said: “We’re confident that Connor is going to stay. I’ve spoken with Gillingham and think both parties are happy.
Essam formed a new defensive partnership with fellow loan signing Ainge at the weekend and despite being in its infancy, he thought the signs were promising.
He’s now hopeful that with a few more games under his belt, Town fans will start to see the best of him.
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