LONDON -- Trea Turner and the Phillies wouldn’t be surprised if he is back in the lineup within the next week.

There are more hurdles to clear before the Phils activate him from the 10-day injured list, but there is optimism he can finish his recovery without a setback or a rehab assignment. Turner has not played since May 3, when he strained his left hamstring.

“We’re getting close,” Turner said before Sunday’s London Series finale against the Mets at London Stadium.

Turner and Phillies manager Rob Thomson said he is running at about 75-80 percent of full speed, which is where he was in Colorado late last month when he suffered a setback.

“I’m in the same place, but a little better,” Turner said. “In Denver, I was really tight. I felt like I could still feel my injury, where I injured it. Now it’s not that. I’m at that same threshold, running with the same intensity, but the feelings are different, which is a good thing.

“I feel more comfortable doing stuff now than I did then. Then, I felt like I was pushing through certain things. It’s probably why I had that little setback.”

Turner is unlikely to go on a rehab assignment before the Phillies activate him from the IL, according to Thomson and Turner. (Turner has the right to refuse an assignment.) Bryce Harper chose not to go on a rehab assignment last year, when he missed the beginning of the season following Tommy John surgery.

In the past, it was an automatic step for a player after missing so much time.

But times are changing.

“Where I’m at in my career, I’ve been on a couple rehab assignments before and I never truly felt they helped,” Turner said. “It’s more checking boxes and making sure they feel good. I’ve been honest with them every step of the way. If something bothers me, I tell them. If it doesn’t, I tell them. I prefer not to do it. The swing feels good.”

The Phillies have a Trajekt machine in the home clubhouse at Citizens Bank Park, which simulates real pitches from real pitchers. Turner has been using it.

“I honestly think it’s way harder,” Turner said. “Oh my God, it’s impossible. But now, there’s so many drills I’ve learned since 2018-19 with the Nats, Dodgers and here, to simulate things and have your brain adjust. It’s not just going out there and hitting 50 mph BP. Speed up, slow down, different pitches. I’m not saying I’m going to be locked in the second I get back, but I feel good.”

Turner was batting .343 with 10 doubles, two homers, nine RBIs and an .852 OPS when he suffered the injury. Edmundo Sosa has done an amazing job in his place. Sosa will return to a utility role upon Turner’s return, although Thomson said the Phillies will try to use him in the outfield to keep his bat in the lineup.

Turner will try to finish the remaining 20-25 percent of his sprinting this week in Boston.

“The injury is -- not gone, but we’re pretty much past that,” Turner said. “It’s getting my brain and body to fire on all cylinders. I don’t know. I told them I would be ready tomorrow or this day or that day. It’s kind of weird. It’s finicky. I’ve never dealt with anything like this. But I feel good.”