Wareham has made 22 career appearances for Woking, scoring two goals.
He made his debut aged 16 on New Year’s Day back in 2020 in a 6-2 loss to Sutton United.
Only five of his 22 outings have been from the start, with his two goals coming as a substitute in the 2-2 draw at Bromley in January.
Dowson did not name Chelsea but says Premier League clearance is the only thing that needs to be sought for his exit to be confirmed.
“Yeah I believe things are getting done,” he told the Woking YouTube channel.
“I don’t think they want to publicise it massively but I believe everything’s in order, it just needs clearance from the Premier League and all that.
“I don’t think there’s any problems with it, I think everything will be getting done and good luck to the lad. Whatever club he goes to, it should get done.
“Every day we think it’s getting done, today whatever, we can’t really say the name but I think everybody will know anyway to be honest.
“But the bottom line is good luck to the kid, I hope he does well, I hope he does very good. It will be good for him, I think he’s got a couple of years to kick on. Fair play to the lad.
“It’s done I think but I think when you go there you’ve just got to get permission off the Premier League and all that. That’s the only snag and I think everything else is done.”
Wareham has been a prolific goalscorer for Woking in their academy setup since joining in 2019.
He also scored for Chelsea’s under-18 side against Aston Villa on April 10.
Dowsonallowed Wareham to join the Blues on trial and he says negotiations are ongoing about what they will receive in return.
“He’s been here for a few years now so we’re negotiating, that’s what we’re doing at the minute, I’m sure they’ll be very fair,” Dowson continued.
“Especially with how the top six clubs are at the minute, [they’ve] been hammered, it would be a massive good thing because we’ll tell everybody how great they’ve been.
“They have been fair. We’ve been very good to them so hopefully they will be very good to us as well.”