The 22-year old Dagenham & Redbridge striker joined the Posh in late November from the League Two club and has been an instant hit with four goals in five appearances.
Gayle netted his fourth Championship goal in Peterborough's 2-1 upset win over league leaders Cardiff City on Saturday and now manager Darren Ferguson wants him to stick around at London Road for a little longer.
"It would be a brave man to try to take him off us now. I'm sure he'll stay with us," he told BBC Radio Cambridgeshire.
"He listens. He picks up things quickly, which is always a sign of a good player. He's going to be a really good player the boy."