The former Beatles star has previously expressed a desire to work with the psychedelic pop duo, but the pair have admitted he hasn't yet contacted them to arrange laying down some tracks together.
Frontman Andrew Wells VanWyngarden told Spinner: "It's been tough. We did play a show with him last summer at NY Park, which was really cool.
"But nothing has really come of the collaboration part of it. We still would really like to do that. We like Paul McCartney's songwriting abilities and musical sensibilities. His bass playing is unreal - he is definitely our favourite bass player."
In the past, the 'Hey Jude' star has stated he would like to take his solo work in a more "dancey" direction with the assistance of the pair, but won't try and contact the 'Kids' hitmakers.
He said: "I like MGMT. I'd like to work on some more dancey stuff with MGMT. But it has to happen organically. We need to talk about it. I can't call them. If they called me, I'd say, 'How did you get my number?'. But I'd do it."