The Magpies will be looking to return to winning ways against the Seagulls after picking up just one point from their last two matches.
Newcastle, who occupy third position, remain on course to qualify for the Champions League, and they can extend their gap to fifth-placed Liverpool to four points with a win on Thursday.
With the chance to move closer to securing Champions League football, the hosts would have been hoping for Longstaff to recover in time.
However, Newcastle boss Eddie Howe confirmed that Longstaff will miss a fourth consecutive game due to a foot injury.
"I think we are quite clear on the injury it is just how long it takes to heal," Howe told reporters at his pre-match press conference. "Sean made good progress yesterday so let's see how he feels today but he won't be part of this game."
Murphy, meanwhile, was an unused substitute in Saturday's 2-2 draw with Leeds United, and there are concerns over his availability.
Commenting on Murphy's injury status, Howe said: "Jacob is probably the only other doubt we have."
The Magpies are also unable to call upon the services of Matt Ritchie, Emil Krafth and Jamaal Lascelles, who are all sidelined with injury issues.
Brighton will travel to St James' Park in a buoyant mood after they thrashed Arsenal 3-0 in their most recent outing, and Howe has admitted that he has "respect" for Thursday's opponents.
"It's one we are looking forward to," the Newcastle boss said. "I think it will be a really good game between two excellent teams.
"I have got a lot of respect for Brighton and what they have done this season. And how they play, watching them against Arsenal in their last match I was hugely impressed.
"I think it's going to be a really tough assignment for us but one at home we are not fearful of, we are going to take a big step forward."
Newcastle have lost only two of their 17 home league games this season, although one of those defeats took place in their most recent home fixture against Arsenal.