Mayweather promotes Davis (18-0, 17 KOs) but says he will not be rushing him into world title unification fights just yet. Lomachenko (8-1, 6 KOs), 29, holds the WBO belt and is already a two-weight world champion after just nine professional fights.
"There's no rush, Lomachenko has to rush because he's 30 years old, so he has to rush," Mayweather said. "This kid [Davis] is still young so we're going to take our time. We're not ducking and diving any opponent, but we're not focused on any other opponents right now. We're not throwing any names out there but whoever takes the fight Gervonta has an equaliser that can change the fight."
It was a clinical finish from Davis -- who is known as 'Tank' -- and Walsh just could not handle the diminutive American's power. Walsh was left on his back after being caught by a series of clubbing left hands to the temple and when he got to his feet he stumbled around on legs of jelly.
Davis, from Baltimore, steamed in to inflict more punishment and -- despite what Walsh said afterwards -- it was a sensible stoppage by referee Michael Alexander.
"Tank don't say much, he likes to do his talking in the ring," Mayweather said.
Mayweather, who admitted it is highly likely he will fight UFC champion Conor McGregor, believes Davis can one day become boxing's biggest star.
"We put him in this position [making a first defence in London] because we believe this kid can fight and he will be a superstar," Mayweather added. "He's still a kid and still growing, we don't know how big or good he can be. One step at a time, we're not going to rush. Everything is a process and takes time. There's a lot of things he needs to learn on the outside of the ropes.
"This kid right here [Davis] is one of the biggest names in boxing and has to be one of the most exciting fighters. He's not even 100 percent -- he will get better. We were saying don't rush the knockout because he's the main event, you have to take your time."
Davis was even talking to Walsh before he exploded into action and let his power shots go later in the third round.
"I took my time, I thought we were going to go the distance," Davis said. "I was telling him he was too slow."
Walsh, 31, from Cromer, thought the stoppage was premature and wants a rematch, but that seems unlikely.
"That was a bad stoppage," Walsh said. "He's very fast and very active but it was too quick. He won fair and square but in England sometimes they stop the fight too early. I'm not saying the result would be different, but give me a chance, I would love to fight him again for next to nothing."