Messi missed Argentina's 2-0 win over Peru due to an injury he sustained in his country's second group game against Chile.
The Inter Miami forward managed to play the full duration of the 1-0 win despite receiving treatment due to a thigh issue.
Speaking after Monday's victory against Peru, Argentina's assistant coach Walter Samuel appeared hopeful that Messi would recover in time for the quarter-final.
Scaloni comments on Messi availability
However, Scaloni, who will be back on the touchline following a one-match ban, has admitted that a decision is yet to be made over the extent of Messi's involvement in Thursday's meeting with Ecuador.
"We will train in a couple of hours, and then we will decide," Scaloni said in his pre-match press conference. "One more day is always better, yesterday we had good sensations and today we will decide. Based on today's answer, we will decide if Messi plays."
"I haven't spoken with him about the situation, I will talk to him today given it's match day -1. I thought it was fair that he took his time and train as much as possible. After talking, we will decide. I haven't talked to him, so we don't know if he will play."
Argentina's all-time appearance holder and record goal scorer has never missed a Copa America knockout game since making his tournament debut in 2007.
Could Martinez and Alvarez start together?
While Argentina will make a late decision on Messi's availability, Scaloni will have to decide whether to start both Julian Alvarez and Lautaro Martinez in the quarter-final clash.
Alvarez was given the nod for Argentina's opening two group matches, before Martinez started against Peru following two successful substitute appearances.
The pair started together in the 1-0 win over Ecuador in a friendly last month, and it is an option that Scaloni will consider ahead of Thursday's fixture.
"They've played together against this rival, and we will decide after today's training," Scaloni added. "They've worked well, and it's an option. But we will see how everyone is today, especially Leo, and we will see."
Alvarez has registered one at Copa America 2024, while Martinez is currently the tournament's top scorer after netting four goals in his three appearances.