Valverde, who took charge at the Nou Camp in 2017, faces the axe after Saturday’s Copa del Rey final defeat to Valencia.
Despite guiding Barcelona to La Liga success, the 55-year-old’s failure to land the Champions League and domestic cup has put him in the firing line.
Reports in Catalunya suggest Valverde will be binned today.
But, according to Spanish journalist Eduardo Inda, Messi could save the head coach’s skin by speaking out in favour.
Speaking on El Chiringuito de Jugones, Inda said: “The only thing that could save Valverde is for Messi to send a strong message stating the continuity of the coach, if Messi says that, he can save himself, before saying it softly, but he does say it forcefully.”
Barcelona were on course for the treble after a 3-0 victory against Liverpool in the first leg of their Champions League semi-final.
A second-leg meltdown at Anfield, however, saw them dumped out of the competition in humiliating fashion for the second season in a row.
Beating Valencia in the Copa del Rey would have waylaid any doubts over Valverde’s future but the 2-1 defeat has seen fans turn.
Catalan broadcaster RAC1 claim Valverde will be chopped on Tuesday after the club’s board decided a new direction was needed.
A four-man shortlist including Arsenal boss Unai Emery and Belgium chief Roberto Martinez has reportedly been drawn up.
Messi spoke out in favour of Valverde before the Valencia defeat.
“I would like [Valverde] to continue,” the Argentine said.