Lennon is hopeful of finalising personal terms with on-loan goalkeeper Forster to activate a permanent switch from Newcastle United.
"Fraser's agent is in tomorrow, so we are hoping to move things on pretty quickly," said Lennon. "He has been excellent over the past two years and we would like to keep him.
"I think it's too straightforward to say we could get Fraser and Gary both sorted this week. There is still a bit of mileage in both."