The Cherries assistant boss confirmed that manager Lee Bradbury was set to hold talks with the Glenn Hoddle Academy over securing the duo's services.
Williamson, who has already stated his desire to stay at Dean Court, was drafted in from the academy on a short-term contract for the final four months of last season.
The striker made five substitute appearances in the first team and did enough to earn an offer of a new one-year deal, with an option of a further season.
Goalkeeper Lumley spent the closing weeks of the 2010-11 campaign on trial with Cherries.
With Dan Thomas set to spend next season on loan with Dorchester Town, Bradbury last month confirmed that he wanted to sign Lumley as competition for Shwan Jalal.
Lumley started his career in the youth ranks at Wolverhampton Wanderers before joining Hoddle's Academy in 2008.
Providing an update on the Glenn Hoddle Academy prospects in an interview with Cherries Player, Fletcher said: Ben Williamson and Billy Lumley are tied to the Glenn Hoddle Academy.
Bradders is speaking to them early next week.
Everything is there for the green light to go ahead. There are always a few hiccups along the way and we are just trying to sort out a few things.
In an ideal world, we will have Ben and Billy and we will keep the rest of the squad.
We will sit and wait and see what happens.