"I think President Trump and the new administration need to be wary of Russian promises," Brennan told the BBC broadcaster.
Speaking about the situation in Syria, he said Moscow was still key to resolving the situation there, however it had been "disingenuous" in its negotiating tactics and not willing to strike a deal to end the hostilities.
"I do not have confidence that the Russians are going to relent until they are able to achieve as much tactical battlefield successes as possible," Brennan said.
During his presidential campaign, Trump has hinted at working more closely with Russia on a number of issues.
On Tuesday, Kremlin spokesman Dmitry Peskov said that Russian President Vladimir Putin and Trump share the outlines of their foreign policy approaches despite differences on details.