The Leeds United hitman hasn't made a decision over his international plans it seems.
Republic of Ireland boss Mick McCarthy still hasn't handed the England-born striker a call-up, despite Bamford seemingly intimating that he would be willing to switch his international allegiances.
McCarthy said last week that the onus is on the Leeds hitman to pick up the phone and give him a call, insisting that he wouldn't be chasing the 25-year-old striker.
And former Whites marksman Keane, who is Ireland's most prolific goalscorer of all time, has told The Irish Sun that it winds him up when a manager has to go after running after a potential player.
"I'll tell you with Patrick Bamford, he should be chasing us. He should want to come here. If he doesn't want to, no problem," he said.
"We shouldn't be chasing people, by the way. That's what f***ing winds me up. We shouldn't be chasing people.
"They should want to play for us. If they don't, then no problem. Why should we go and chase people? We are f***ing Ireland."
Whether he still feels as if he has a chance to represent England remains to be seen, but if he hasn't declared for the Boys in Green by the next round of internationals in September then it might be too late.
Bamford had an okay first season at Elland Road, netting nine Championship goals in 16 starts last term.
It was an injury-hit maiden year in West Yorkshire but, despite falling foul of United fans toward the end of the campaign, the former Middlesbrough star can be a big player for Marcelo Bielsa next season.
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