It was reported back in January that Rangers were targeting Lovelace, who made his first-team debut for Millwall aged just 15.
He has since made four competitive appearances for the Lions and won’t turn 17 until January.
Millwall boss Gary Rowett expressed his desire to keep Lovelace at the London club but realised there was an “inevitability” about a transfer with so much interest from bigger clubs.
“The club have made it clear that we would love Zak to be part of what we do next year and on a full-time basis,” Rowett said.
“There is an inevitability, unfortunately, that some of your better young players get poached by other clubs. To a certain degree those fees are a little bit out of your hands.
“For those types of players there is a structure in place with the likes of Premier League teams or other teams trying to sign those players.
“Until they have signed professional contracts you are always open to them coming in and pinching them, like they have with some of the other youngsters that have been well-documented over the years."
Landing Lovelace is a big win for Rangers, with their own teenage striker Rory Wilson set to depart for Aston Villa in what could be a complex cross-border deal.