The 22-year-old spent last season on loan at Celtic after being brought to the club by former boss Brendan Rodgers.
West Brom felt the youngster would be able to gain valuable experience working with Rodgers and hoped the Scotland international would come back a better player.
However, following Rodgers’ departure to Leicester City in February, Lennon took over at Parkhead and the Baggies were left outraged by how the new Hoops boss treated Burke.
“He won’t be going anywhere near Celtic with the current manager,” West Brom technical director Luke Dowling said when asked if Burke could return to Scotland.
“We sent Olly to Celtic in good faith with Brendan Rodgers and Lee Congleton some really good people up there that wanted to take Olly and wanted to play him.
“Once Brendan left to go to Leicester the treatment he got from the manager that’s in place now is something we don’t expect from one of our players.
“He won’t be going anywhere near Celtic FC.”
When pressed for more details about the fallout between the clubs over Burke, Dowling said: “They know what’s gone on and Olly certainly knows what’s gone on.
“It’s just something we’re not happy with at all.”
West Brom recently announced the appointment of Slaven Bilic as their new boss, who will replace Darren Moore.
The 50-year-old Croatian returns to English football after being sacked by West Ham in 2017.
And according to Dowling, Bilic is looking forward to working with Burke as West Brom seek to return to the Premier League.
“We currently have a new manager that’s excited to start working and looking at Olly,” Dowling added.
“We believe he’s got an opportunity back here with a new manager in place.”
West Brom, who finished fourth in the Championship last season, are expected to sell Venezuelan striker Salomon Rondon, who spent last season on loan at Newcastle.
The club want to cash in on Rondon while they can, rather than risk losing him for nothing in 12 months.
“We’re quite happy to say that we will sell Salomon,” Dowling said.
“We don’t want a player that’s had a season like that staying around with us and walking away on a Bosman.
“Salomon has had the taste of Newcastle. He went back to a Premier League club and if he plays in England that’s where he wants to be. As we understand it Newcastle still have an interest in him.”