The Barcelona captain fell awkwardly on his right arm mid-way through the first half of their 4-2 La Liga win over Sevilla on Saturday.
And Messi was forced off with what was later confirmed as a fracture of the radial bone, with the Argentine predicted to miss three weeks of action as a result.
But Marca report that with Messi scheduled to begin his recovery today, he will first face further assessment.
The Spanish newspaper claim that on Sunday night at home with his family Messi was still in significant pain due to the problem.
It is claimed the 31-year-old is keen not to rush a return and that combined with Barca staff they will look at when is best for his return, although the initial return date has been pencilled as a clash with Real Betis on November 11.
Yet Marca claim that if all goes well then Messi could even return earlier the same week when Barca travel to Italy to face Inter Milan in the Champions League group stages on November 6.
It is said Barca would be taking a risk if Ernesto Valverde was to restore Messi to the team for that trip, but that the possibility of an early return has yet to be ruled out.
But equally, the Catalan outfit could decide to protect Messi until after the international break – which follows immediately after facing Betis.
Barca’s first game back from a two-week break, in which Messi is highly unlikely to play for Argentina having missed their four matches so far this season, sees them face Atletico Madrid in a mouthwatering showdown.
The magnitude of that encounter could see Barca keep Messi in bubble wrap to make sure he is in perfect condition against Atleti.
Messi has missed 61 matches since the start of the 2010-11 season through injury, suspension and rest – Barca losing only six, with four in La Liga, and by contrast winning 49.
But Ernesto Valverde could not hide his concern over the prolonged absence of his skipper.
The Spanish boss – whose side had gone four league games without a win before beating Sevilla – said: “Of course he’s a major loss. We know what he does for us and what our opponents think just by seeing him on the pitch.
“We must prepare ourselves. We have the players to cover for him, but we have some very tough games coming up.
“In the past we have had games without him and have always tried to maintain our style.”
Barca return to action against Inter Milan at the Nou Camp on Wednesday (8pm) with Ousmane Dembele hoping to take Messi’s place in the starting line-up.