Gareth Bale and a number of senior members of the Wales team have reportedly urged manager Chris Coleman not to quit.
The Dragons suffered disappointment on Monday night when they were beaten 1-0 by the Republic of Ireland in their final World Cup qualifier.
The result meant that Wales will not be competing at Russia 2018, having failed to secure automatic qualification or a playoff spot.
After the match, Coleman revealed that he needs to take some time before deciding on whether or not to continue on as manager of his national side.
According to Sky Sports News, Bale, who did not play in the nation's final two qualifiers due to a calf injury, joined a number of his teammates in a meeting with Coleman, in which they advised the coach to stay put.
The 47-year-old, who has been in charge of the team since 2012, guided Wales to a historic semi-final at the European Championships last year.