The Magpies play German Third Division side Chemnitzer on July 13 and the Monte Carlo club have been in discussions with United over a second game as part of their own pre-season training plans.
Monaco will be in eastern Germany at the same time as Newcastle and already have games against Wacker Innsbruck (July 3) and Dynamo Kiev (July 9).
Monaco are a Second Division side these days andare managed by former Chelsea boss Claudio Ranieri.
Newcastle's pre-season list of games includes a trip to Portugal to participate in the Algarve tournament.
Alan Pardew’s side will take on former Champions League winners FC Porto and Greek giants Olympiakos.
The game with Olympiakos takes place on Friday, July 27, before Newcastle face Porto 24 hours later.
So far the only friendly in the UK will be against Cardiff City on August 11.
Pardew will also send an XI to face Gateshead on August 1 in a fixture that featured several first-team players last summer.