The West Ham United defender, 21, spent most of last season on loan with Bolton Wanderers, but bid farewell to the Championship side last week in order to return to his parent club.
But a long-term future in East London might be in doubt for Burke as The Mirror reports that West Ham debate whether to loan him out again or sell him outright.
The report adds that Rangers and Leeds are willing to sign him up on a permanent basis, though Sheffield Wednesday lead the race in regards to getting him on loan.
Aston Villa, who reached the playoff final last night by beating Middlesbrough, are also in the mix.
New Gers boss Gerrard made Scott Arfield his first signing earlier this week, and signing the highly-rated Irons centre-back - who can also play right-back - would certainly indicate that the Liverpool icon is wasting no time in assembling his squad for next season.
Leeds, meanwhile, are in the market for someone of Burke's ilk, having seen Matthew Pennington return to parent club Everton last week following a mixed season-long loan in West Yorkshire.
Burke, who has made 15 appearances for the capital club, is contracted to West Ham until 2020.
Have something to tell us about this article?