The 54-year-old was dismissed on Wednesday after a reported falling out with club owner Peter Lim.
Former Barcelona and Real Madrid midfielder Albert Celades, who was an assistant coach to Julen Lopetegui at the Santiago Bernabeu last year, has been tipped to take over at Mestalla.
Marcelino was appointed as Valencia boss in May 2017 and led the club to a fourth-place finish.
His position came under threat 12 months ago during a difficult start to 2018-2019, but the club kept faith in the former Villarreal boss and was rewarded when it ended the season by winning the Copa del Rey final against Barcelona and clinching a UEFA Champions League spot.
Valencia has taken four points from three games this term but it was reported in Spain that Lim called club president Anil Murthy for an emergency meeting in Singapore on Wednesday after deciding to sack Marcelino.
There are also suggestions sporting director Mateu Alemany could be dismissed.