Midfielder Reed, 21, has made eight appearances for Pompey after moving from the Black Cats at the end of January and 29-year-old Crawley full-back Cooper has played seven times since rejoining the club where he began his career.
Cooper is currently sidelined by a hip injury but caretaker boss Guy Whittingham expects him back in action soon.
He said: "Shaun has returned to light training. Tuesday's game (against MK Dons) will come too quick for him, but we're hoping he might be available at the weekend."
Defender Sam Sodje's latest contract is also up, but he is suspended for the next three matches following a red card against Oldham on Saturday.
"It's out of character, but we'll deal with him how we see fit," added Whittingham.
"It's not a case of ripping up his contract, though, because he's played well in the last few games."