"Good luck to Biden in dealing with President Putin - don't fall asleep during the meeting, and please give him my warmest regards!", Trump said on Thursday.
The former US commander-in-chief also shared his own positive experience with the Russian president during a summit in Helsinki.
"As president, I had a great and very productive meeting in Helsinki, Finland, with President Putin of Russia. Despite the belated Fake News portrayal of the meeting, the United States won much, including the respect of President Putin and Russia", Trump said.
Putin and Biden will meet in Geneva on 16 June to discuss a wide range of bilateral issues, including global strategic stability, arms control, the Nord Stream 2 pipeline, and Ukraine.
Commenting on the anticipated summit, Russian Foreign Minister Sergei Lavrov said Moscow hopes that Washington will review its past mistakes before the meeting. The top diplomat added that Russia is open for a "frank dialogue".
Bilateral relations have deteriorated recently over a series of accusations against Moscow, including allegations of cyberattacks and its alleged meddling in the US elections. Russia has dismissed all accusations as lacking any proof, while also introducing "mirror" measures in response to anti-Russia sanctions imposed by Washington.