The 20-year-old, handed his debut by head coach Paul Heckingbottom in the final weeks of the season, is the only member of the senior Elland Road squad out of contract this summer.
United are keen to keep hold of Pearce, who made five appearances for the first team and scored his first goal against Barnsley in last month’s 2-1 home win.
However, Bournemouth and Everton are also understood to be interested in Pearce, who signed a 12-month deal last summer.
He has been at Leeds for four years, the Yorkshire club having snapped up the defender on his release by Everton.
Under-23 players Kamil Miazek and Clarke Oduor have also been offered new deals.
Four youngsters will be released come the end of next month. Moses Abioye, Matthew Keogh, Moise Kroma and Romario Vieira, the younger brother of United first-team player Ronaldo Vieira, will all depart the club.
United will be entitled to compensation under Football League rules if Pearce is lured away.
Underlining the potential that Pearce has shown in a Leeds shirt, he was yesterday named in the England Under-20s squad for the Toulon Tournament.
Fikayo Tomori, the Chelsea defender who spent the season on loan at Hull City, is also in the 20-man party for a competition that the Three Lions have won in each of the past two years.
Aidy Boothroyd’s side kick off against China at Aubagne’s Stade de Lattre a week today.
England will then be back in action three days later when Mexico are the opponents in Salon, before the group fixtures are rounded off against Qatar on Friday June 1 at the Stade Parsemain in Fos-sur-Mer.
The final will take place on June 9.