The Football Association of Wales (FAW) wants Chris Coleman to remain as manager of the national team.
His contract expires next summer and they are set to begin talks over his future in the next couple of weeks.
Coleman, 47, took over in January 2012 and guided Wales to the semi-finals of Euro 2016 but they failed to qualify for the World Cup following Monday’s 1-0 defeat by the Republic of Ireland.
The FAW is aware of the Welsh squad’s desire for him to stay.
His current contract was renewed just before the start of Euro 2016 and BBC Sport Wales has learned the FAW want to extend it beyond the end of November, subject to negotiations over a new deal.
A number of players, including Gareth Bale, urged Coleman to stay in the wake of the Republic of Ireland defeat.
Chris Gunter, the most-capped Wales player in the current squad, hailed Coleman as the “greatest Welsh manager of all time”.
The FAW is also aware of the view of Wales fans who have overwhelmingly made clear they want Coleman to remain.
After the defeat against the Republic of Ireland, Coleman said he would let “the dust settle” in order to mull over his future.
But focus has now turned to the Uefa Nations League, with the draw for that new competition on 24 January, so negotiations would need to begin soon.
Wales have two friendly matches planned for November, with the United States and Mexico among possible candidates.