After winning three world titles in three divisions, Garcia will challenge Sergey Linnets for the IBF super-lightweight title.
Lomachenko, meanwhile, retained the WBO World super featherweight title earlier this month after Guillermo Rigondeaux retired.
Mayweather, who has now hung up his gloves, claimed world titles in five weight divisions during his undefeated 50-fight career.
And the American is convinced that Lomachenko needs to fight Garcia if he wants to prove how big he really is.
“If Lomachenko is what they say he is, I think they should make him and Mikey Garcia,” Mayweather said.
“I mean, that’s just my honest opinion.
“I think Lomachenko and Mikey Garcia should lock up.
“Great fighters always move up. We call that legendary. A lot of fighters are taking shots at Tank.
“At the end of the day, Tank is not perfect, but his boxing record is.”
Garcia meanwhile, has set his sights on becoming as big as Mayweather one day.
“I know that I have the possibility to be the biggest star in boxing like a Floyd Mayweather, and I think I’m on track to accomplish that,” Garcia said.
“I don’t see a lot of guys in the sport with the resume of accomplishments that I have.
“I’m going to continue take on the best and beat my opponents convincingly.”