The Paisley side have already borrowed left-back Paul Dummett and midfielder Conor Newton from the Magpies as part of an affiliation deal between the two clubs.
Both players played key roles as Lennon's side secured their first major trophy in 26 years with victory over Hearts 3-2 in the Scottish Communities League Cup final.
The pair have now been rewarded with new deals on Tyneside and Lennon revealed he had spoken to counterpart Alan Pardew after Tuesday's friendly between the sides about how Campbell might benefit from a similar spell.
"I looked at their squad on Tuesday night and even when they were taking guys off they were replacing them with players who are top drawer," Lennon said.
"Conor Newton came on in the second half and he did very well for us last year and we now have a strong affiliation with Newcastle.
"Young Adam Campbell looked lively when he came on and he is a player we are more than aware of."