The Tottenham hotshot, who worked under new [Baggies](https://www.expressandstar.com/sport/football/west-bromwich-albion/) boss Ryan Mason in north London, spent the second half of last season at The Hawthorns.
And reports in north London claim Mason's new club are interested in a second loan for the 20-year-old frontman.
Albion are looking to bolster their forward line options this summer with Josh Maja, Daryl Dike and Devante Cole current natural centre-forward options.
Lankshear failed to score in his loan last season, in which he made 11 appearances for the Baggies, though just four of those were starts after the highly-regarded youngster had initially struggled to break into the side behind the preferred Adam Armstrong.
But the striker, who made his Spurs senior debut and scored his first goal earlier last season, caught the eye of coaches and fans when offered a start in April.
Albion are understood to be admirers of Lankshear and believe he has a bright future.
New boss Mason's pre-season started this week as his squad checked in for testing on Wednesday. So far the Baggies have captured Liverpool defender Nat Phillips on a three-year deal in a summer expected to be quieter than the more significant turnover 12 months ago.
Speculation has been rife of Mason's potential to return to the Tottenham Hotspur Stadium for loan moves of the club's brightest youngsters. Attackers Jamie Donley, 20, Mikey Moore, 17, and midfielder Alfie Devine, 20, are viewed as top prospects.
A striker linked with The Hawthorns who is not expected to be Black Country-bound is Hearts goal machine Lawrence Shankland.
The 29-year-old frontman is out of contract at the Edinburgh outfit, where former Baggie Derek McInnes is manager.
It had previously been suggested Albion were a potential suitor for Shankland, but it is understood that claim is wide of the mark.