Man City captain Walker wants to leave, says Guardiola
Walker, 34, has won 15 major trophies, including six Premier League titles, since joining City in a £50 million ($61 million) deal from Tottenham in 2017.
"Two days ago Kyle asked to explore the options to play abroad and end his career," said Guardiola after Walker did not feature in his side's 8-0 FA Cup third round win over Salford.
"In his mind, he would like to explore it, to go to another country, to play the last years (somewhere else) for many reasons."
Guardiola confirmed that Walker had also asked to leave at the beginning of the 2023/24 season amid interest at the time from Bayern Munich.
However, the England international was convinced to stay and signed a new contract until 2026.
"He asked (to go) two years ago after the Treble. I think Bayern Munich wanted him but the offer wasn't good enough and I and the club asked him (to stay) because of how important he is," added Guardiola.
"We cannot understand the success we've had these years without Kyle. It's impossible.
"Having a right-back (like him) gave us something that we didn't have and he has been amazing."
Walker, who has been capped 93 times by England, has also been part of the Three Lions squads that have reached the last two finals of the European Championship.
However, his struggles for form and fitness have played a part in City's disappointing season so far.
Guardiola's men won just once in 13 games between October 30 and December 29 to slip out of contention for the Premier League title and exit the League Cup.