The 20-year-old has been regularly linked with a move to Manchester United over the past couple of months.
A report in the Daily Mail earlier this month suggested Rice was Manchester United’s top target ahead of the summer transfer window.
The West Ham midfielder fits the bill for the type of player that Ole Gunnar Solskjaer has targeted since taking over the reins of the club.
Rice is an English talent with plenty of potential to be moulded into a top Premier League star.
The London-born star represented the Republic of Ireland on three occasions in friendlies before Rice decided to switch allegiance to England.
His former Irish coach Keane believes Rice has to make a lot of improvements to his game to become a top player.
“Where he needs to improve, there are plenty of aspects if you think about it,” Keane told ITV Sport on Sunday.
“Over the last few months he has had a lot of praise, I worked with him while he was with the Ireland squad.
“Where does he need to improve, where do you want me to start?
“His positional play I don’t think is consistent enough, he doesn’t stay with runners, he’s sloppy in possession.
“I can go on.”
Rice has been a regular in the West Ham team since Manuel Pellegrini’s appointment at the start of the 2018-19 season.
The England international has featured in all 1080 minutes of West Ham’s Premier League football so far this season to underline his importance to Hammers boss Pellegrini.
The West Ham No41 has scored two goals in 82 games in all competitions over the past three seasons for the east London outfit.
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