Justham, whose two-year deal runs out this summer, has made 14 appearances this season following an injury to first-choice goalkeeper Mark Tyler.
Formerly a triallist at West Ham and Reading, Justham remains keen to continue his progress at Kenilworth Road having helped Luton to a 3-0 win over Hartlepool last weekend.
When asked about the speculation, Justham told Luton Today: “I’ve got a contract in motion and I don’t read all that. I’ll be staying here.
“I’m loving it here. Hopefully I can challenge Mark next year and try to cement that number one place at the start of the season if not during the season, so I’m looking forward to staying here.
“I want to battle with Mark when he’s fit and hopefully I’ve given the gaffer a bit of thinking to do.”