Keane, 45, is understood to have held talks with the Parkhead hierarchy surrounding their current vacancy.
Having resigned as manager of Ferencvaros last month, Keane is currently a free agent.
And despite holding talks over the Celtic job, he is expected to play for Liverpool legends this weekend in a tournament in South Korea, claims Sky Sports reporter Anthony Joseph.
Robbie Keane is still expected to play for Liverpool Legends at the Champions Impact tournament in South Korea this weekend.
The match against Barcelona Legends takes place at the Seoul World Cup Stadium on Saturday. https://t.co/NmmvTFIImy
— Anthony Joseph (@AnthonyRJoseph) June 3, 2026
As a player, Keane spent less than a year on the books at Anfield, registering 27 appearances across which he scored seven goals and assisted five.
His managerial career has thus far led him to Maccabi Tel Aviv, where he won the Israeli league title.
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After joining Ferencvaros in January 2025, he led them to the Hungarian championship, but failed to retain it during his first full season with the club.
Alongside Keane, Celtic have held talks with Martin O'Neill – who led the club to a double last season – over the managerial position, with Wales boss Craig Bellamy also a potential candidate.