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Marquez will also manage FC Goa in 2024-25 before taking up the full-time job.
The All India Football Federation sacked Stimac following India's failure to reach the third round of the FIFA World Cup Qualifiers.
'The sooner Kalyan Chaubey leaves AIFF, the better it is for Indian football,' Stimac said.
Stimac, who was appointed as the head coach in 2019, was in last October given an extension until 2026 by the sport's apex body.
The Real Madrid and Croatia great had a video message for Indian captain Chhetri who will retire after the match against Kuwait on Thursday.
A win on Thursday will almost guarantee the Indian team a maiden appearance in the third round of the 2026 FIFA World Cup qualifiers.
'The retirement decision was not because of physical aspect, I am still fit, running, chasing, defending, the hard work is not difficult, the reason is to do with mental aspect,' said Chhetri during a virtual interaction.
The first list of probables announced on Saturday featured three Keralites - Rahul K P, Vibin Mohanan and Jithin M S.
The list does not feature players from Mohun Bagan Super Giant and Mumbai City FC as they will compete in the ISL final at Kolkata later tonight.
The coach was told by the AIFF committee focus on the games ahead and plan his preparation accordingly.
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