Lineker, in Dublin for an appearance at a Walkers Crisps sales conference, salutes Keane for his Irish record of 54 international goals, but doesn't see him as one of the greats of the game.
The former England captain and current BBC 'Match of the Day' presenter made 80 appearances for his country, scoring 48 international goals.
Lineker also voiced sympathy for the Dubliner, who has been regularly criticised despite his long service to Ireland and his goal-scoring feats in club football.
"He's been a journeyman, there's no doubt about that, but Robbie's a top-class centre-forward and goalscorer," said Lineker. "He's a trier. He's not probably the player you'd put in your all-time greats or anything, but he's on the next rung down. He's a first-class Premier League player."
Irish fans and media have at times had a 'love-hate' relationship with Keane and the striker didn't emerge with any kudos from the European Championships. Coping with the brickbats comes with the job, insists Lineker.
"That's part and parcel of being a footballer, isn't it? It's a fickle game. One minute things are going really well for you, the next minute nothing will happen for you," he said. "It's the nature of the sport, but Robbie's been a very consistent performer for Ireland. Fifty-four international goals is a quite phenomenal achievement.
"He's always turned up, he's always put in the effort for Ireland and even in recent times, when they've struggled a little bit in the last few months or so, he's been ever-present."
Keane – who lines out for LA Galaxy against Houston Dynamo in the MLS Cup final tomorrow night – is likely to return for another spell in the Premier League in January, with Aston Villa already being linked with a move.