Mark Dodson, the SRU chief executive, revealed last week that he is planning further talks with the head coach.
Townsend took the Scotland helm in May 2017, signing a three-year contract in July 2018.
Asked if he could sign a new deal soon, Townsend said: “Yeah that would be great if it happens.
“We’ve been in discussions for a few weeks now. So I’m hopeful that something could be agreed or announced over the next few weeks.”
Asked if the new deal would take in the next World Cup, Townsend added: “We’ll see. But 2023 would be great, because obviously it gives everybody a target for that World Cup, to work together.
“I think everybody in this playing group should be available for the next World Cup, and being in the northern hemisphere (in France) and being not too far, it would be great if we do stick together until then.”