Irving (right quad contusion) and Morris (bruised left hip) are both listed as questionable when the Eastern Conference-leading Celtics take on the Raptors, who are two games behind in second place.
Both, however, made the trip to Toronto and Morris has indicated that he is ready to play Tuesday.
Shane Larkin (sore right knee) and Marcus Smart (lacerated right hand) both remain listed as out.
The Celtics continue to win despite the injuries. They are on a four-game winning streak after Al Horford's buzzer-beater gave them a 97-96 victory over the Portland Trail Blazers on Sunday. The Celtics trailed by 16 points at halftime.
Irving has missed three games in a row and Morris the past two.
"Coach (Brad Stevens) called a play for Jaylen (Brown), and as he's calling it he's saying, 'Keep the ball, keep the ball. Go score,' " Horford said of his winning shot. "They read it perfectly because I wanted to hand him the ball and they stayed very tight to him. So once that happened I was very aggressive, went to a go to move. It was like, 'I've got to find a way to score.' Took my time. That's a shot I work on a lot, and it felt good that it went in."
The Raptors kept pace with the Celtics when they defeated the Memphis Grizzlies 101-86 Sunday in a game that started at noon.
The Raptors depended on their bench for this win as Delon Wright led them in scoring with 15 points and Fred VanVleet had 13. DeMar DeRozan led the starters with 13 points.
Raptors coach Dwane Casey praised the young players on the team.
"I thought they played well," Casey said. "The starters must have hung out last night, but you know, these are the scariest games and the fact that you look out there and you don't see Mike Conley, you don't see (Chandler) Parsons, whoever it is with Memphis, and human nature is to let down and I was afraid of that at the start of the game and it happened.
"But our young guys, they brought the energy, they did what they were supposed to do, and their plus/minus was off the charts, 25, 26, 26, 36 with Delon (Wright). So, they came in and did their job."
"Give them credit for the game today," DeRozan said. "They did what they are supposed to do. I made a joke that the old guys can't get up this early in the morning for the game. They came out with a lot of energy and they did what they were supposed to do, and they got us this win (Sunday)."
The Raptors had C.J. Miles back in the lineup after he had missed three games with a sore right knee and he had two points in five minutes.
The first time the teams met this season was Nov. 12 when the Celtics defeated the Raptors 95-94 at TD Garden.
Horford led the Celtics with 21 points in that game. Boston came up with a defensive stop as the clock expired to preserve the victory. DeRozan scored 24 points for Toronto.
The Celtics are a strong defensive team.
When asked Monday after practice how his team could combat Boston's defense, Casey said: "Make sure we space the floor. Play aggressive, physical offense. We've got to set solid screens. But most of all, we've got to play with force."
Casey felt that in the first meeting with the Celtics did too much standing around and "weren't moving the ball."
The Celtics, meanwhile, have shown they are a difficult opponent even when depleted by injuries.
"Just shows the character of our team, that we're always ready, can always count on one another," Terry Rozier said. "We have eight guys, 10 guys on the bench. Smart not playing is still there giving us encouragement -- ways we can do better. We're still a unit. Obviously, Kyrie is not going to play every game, so we're going to have to have that next-man-up mentality."