Peralta, a 24-year-old Honduras international midfielder, is a free agent after leaving Deportivo Vida in his homeland.
Left-back Smith is also available on a free after his contract with MLS side Portland Timbers expired at the end of last year.
The 27-year-old has been training with Rangers for the past few weeks with a view of sealing a permanent return to the club where he began his career in 2002.
Gers boss McCoist, who is planning for a campaign in SFL2 next year, confirmed that both deals could be sealed within the next week.
"We are close now with Arnold," said the 50-year-old. "We watched him playing for Honduras against Panama and he did well. Terms have been agreed with Arnold so hopefully in the next three or four days we'll push that one through.
"Arnold is very aggressive and gets about the park well so I think he would blend in with the rest of the midfield and be a good signing."
Regarding Smith, McCoist added: "There's definitely an interest in Stevie. It's good to have players who have experience and who know the club so that we, as staff, can rely on them to go and play.
"I'd like to sign Stevie. He was turning up for training there and we tended to forget he wasn't a signed player but hopefully that will change."