The Scotland international fuelled speculation that a deal is already being discussed by admitting it would be “amazing” if the chance arose to return to The Den.
However, speaking ahead of United’s visit to Queens Park Rangers on Friday, manager Paul Heckingbottom insisted Burke will only be allowed to depart if a suitable bid is received.
“Unless there’s an offer or an option that benefits us and Oli - it also has to benefit us - then he is our player and will be coming back to us,” he said. “That’s the situation, as everyone knows and would expect.”
Despite adopting a hardline stance towards the issue of Burke’s future, Heckingbottom is still expected to sanction the forward’s exit when the outcome of United’s push for the play-offs is known.
Sixth in the table with two matches of the regular season remaining, they are three points ahead of Gary Rowett’s side who are also hopeful of gaining promotion.
Although Heckingbottom has yet to receive his recruitment budget for this summer’s transfer window - something he hopes to clarify during one of his upcoming meetings with chairman Yusuf Giansiracusa - the 44-year-old’s comments regarding Burke almost certainly mark the start of a process designed to hike up the player’s value.
Although he struggled for both form and regular first team football after joining United from West Bromwich Albion 19 months ago, Burke has emerged as an important member of Millwall’s squad since heading to the capital in January. His strike against Birmingham City last weekend means he has now netted twice in his last four appearances, having also found the back of the net during a 4-1 win over Barnsley.
“Getting clarity and working on the budget and the finance, that’s something we want,” said Heckingbottom. “We want that clarity and it’s something we’ll hopefully be getting soon. Then we can take good decisions about what we can do going forward.”