The pair have been back in training recently as they continue their recoveries from knee injuries.
Britton, who has made 94 Premier League appearances for Swansea, is still waiting for his first outing this term after suffering a stress fracture on Swansea's pre-season tour of the United States of America.
Spaniard Amat, meanwhile, has been sidelined since being substituted at half-time in a 4-2 defeat at Chelsea on September 13.
Speaking ahead of Swansea's visit to Arsenal on Sunday, Monk said: "Leon Britton is back in training and so is Jordi Amat.
"We'd have to assess whether they're ready but they're all up for selection."
Swansea currently sit sixth in the Premier League and can leapfrog Arsenal with a win at Emirates Stadium.
Monk added: "The team are on track to where I want them to be, they're progressing nicely, taking information on and are at a good level.
"They've played some great attacking football, played the Swansea way, and five clean sheets is pleasing from a defensive point of view.
"But we still have a long way to go to get to where we want to."
