The Saints have extra funds available following their Scottish League Cup success, and are looking to put them to good use.
Steven Thompson, David van Zanten, Marc McAusland and John McGinn have already penned new deals and the intention is to push on with further extension talks.
Samson and Teale are considered to be integral to the club's cause, and Lennon admits efforts are being made to end any uncertainty regarding their future.
He said: "We've started negotiating with Craig's agent and I've also spoken to Gary.
"We're also well into talks with Paul McGowan and hope to get that over the line shortly."