Longstaff has featured regularly in the Newcastle midfield this season, registering three goals and four assists in 40 competitive appearances.
However, Longstaff has missed the club's last two matches after he sustained a foot injury in a 4-1 win over Everton last month.
Speaking in his pre-match press conference, Howe has revealed that Longstaff will miss Saturday's trip to Elland Road, and he admitted that he is unsure if the 25-year-old will play again this season.
"He went to see a specialist," Howe told reporters. "I think there were a few concerns that there may be some sort of structural damage in his foot.
"There wasn't, which was good news, but there is a bit of damage to one of the ligaments. He's being rescanned today actually, which we hope will show an improvement.
"It's slightly unclear when he'll be back, but it's not a long-term issue at all, but just whether we can get him back before the end of the season.
"We could see him as early as next week potentially if he improves really quickly, (or) we might not see him at all. It's unknown, but thankfully there's no serious issue, it's just time and letting that ligament heal."
Howe also revealed that Matt Ritchie will miss the rest of the season after suffering a knee injury in training.
"Matt's picked up a knee injury," the Newcastle boss added. "I don't think it's too bad, but I think it will keep him out for the rest of the season."
With Ritchie out of contract at the end of the season, there is a possibility that the 33-year-old has played his last game in a Newcastle shirt.
After losing 2-0 at home to Arsenal, the Magpies will be looking to return to winning ways when they face a Leeds side managed by former Newcastle boss Sam Allardyce.
Newcastle head into the weekend in third position in the Premier League table and are three points clear of fifth-placed Liverpool, who have played a game more.