Centre-back Amoruso has been sidelined since October with a knee injury which required surgery whilst midfielder Reid has been out since December with a hamstring injury.
"Lorenzo and Steven will be joining in with the rest of the group this week, then we'll see where they are after that," said Rovers boss Graeme Souness told the Lancashire Evening Telegraph.
"The Arsenal game may come a touch too early for them but the fact they are back in training again is good news for us because they've both been out for so long."
"Lorenzo will probably think he's in contention for Arsenal because he won't be keen to play reserve-team football,
"But that gives you an indication as to how close he is.
"As for Steven, he has started running now and he looks ready to join in with the rest of the group."