Lennon's already told the 24-year-old he wants to know by early April how he sees his future. But Forster - 21 clean sheets in 40 appearances - wants instead to wait until the season's over.
He said: "I haven't spoken to anyone back at Newcastle for a while and I'm not really thinking about next season yet.
"I'll wait until summer before I sort that. There are more important things to concentrate on just now."