Captain Johnny Sexton, prop Tadhg Furlong, lock Tadhg Beirne, scrum-half Jamison Gibson-Park and centres Garry Ringrose and Robbie Henshaw were all unavailable in Rome.
While Beirne has been ruled out of the remainder of the championship, Farrell is confident his squad will be significantly bolstered ahead of the round-four visit to Edinburgh on March 12.
Asked who will be available, the head coach replied: “Not far off all of them. Tadhg (Furlong) is going really well and we would expect him to train Wednesday and Thursday when we’re in camp.
“Jamison’s fit, Robbie’s fit, so we’ve got a good crop of players coming back when it matters.”
Furlong, whose tighthead deputy Finlay Bealham was injured at Stadio Olimpico, Gibson-Park and Henshaw are yet to feature in this year’s tournament.
Although Farrell concedes that situation is far from perfect, he is confident the returning players can swiftly get up to speed.
He said: “Well, obviously, it matters because ideally you would love (for them to have some game time) but how many times have we done this now?
“We’ve done it time and time again in regards of it not being ideal.
“But we pride ourselves on making sure that our training gets people up to speed and we’ll see how they’ll come back into that and deal with all that.”
Ireland have dominated clashes with Scotland during the past decade, winning 11 of the past 12 meetings.
Gregor Townsend’s men will be eager to keep themselves in title contention after Sunday’s 32-21 loss to France ended their hopes of a clean sweep and have the added incentive of playing for the Triple Crown.
“It’s one of the toughest places in world rugby to go and it doesn’t matter what anyone’s record is there, they’re tough to beat there,” said Farrell.
“They’re going for the Triple Crown – that will mean a lot to them, so it has to mean even more to us.”