The Scotland defender expects that he will officially sign his new contract within the next 24 hours.
The 32-year-old was out of contract at the end of this season and that prompted Leeds to enquire about prising the defender to Elland Road earlier this summer. Greer is able to feel flattered by such interest but was always of a mind to remain with Brighton.
"I've been here for three years already and it's been great," said the former Kilmarnock player. "I'm really happy here, so hopefully we can get it all tied up and sorted out this week.
"It [the interest from Leeds] is flattering but it's important, especially when you get older, that you don't let these things take away from your game. I have just been concentrating on Brighton."