The midfielder suffered a painful shoulder problem during a poor challenge on Grady Diangana during the latter stages of Sunday’s season-closing 3-1 Premier League win over relegated West Brom at Elland Road.
While Pope is now unlikely to be fit for the Euros, Leeds believe that Phillips should be fine to feature if picked.
“Leeds United midfielder Kalvin Phillips picked up a shoulder injury in the closing stages of Sunday’s Premier League fixture with West Bromwich Albion,” the club said in an update on Monday.
“This is currently being treated conservatively, however, we remain confident he will be available for Euro 2020, if selected for the England squad.”
Phillips, 25, has become a regular in England squads since last summer following his consistent form for Leeds, going on to earn seven caps in total following his senior debut against Denmark in the Uefa Nations League in September 2020.
Speaking after the win over West Brom, Leeds boss Marcelo Bielsa backed the determined Phillips to make a quick recovery.
“Sincerely I haven’t received any information as to the gravity of the injury,” he said. “I couldn’t tell you if it is severe but I hope he can go to the Euros.
“We all hope it’s something that can be resolved quickly. Knowing the fortitude of Kalvin, I know he has the resources to quicken any problem he has.”
Phillips’ fellow midfielder Jordan Henderson is expected to make the England squad for the Euros after recovering from a groin injury that has prevented him from playing for Liverpool since the Merseyside derby defeat by Everton in February.
Henderson was an unused substitute on the final day of the Premier League season as the deposed champions sealed third place and Champions League qualification for next season courtesy of a Sadio Mane-inspired 2-0 win over Crystal Palace at Anfield.