Declan Rice had a good performance in the win at Everton and encouraging draw at home against Chelsea on Sunday which have lifted West Ham from the foot of the league table.
The world and its wife has had their say on Rice's contract situation.
Rice is now earning £3,000 a week, but West Ham recently gave him an offer of £12,000 a week.
Carragher has now leapt to the defence of Rice, believing the youngster should hold out for the best possible deal, while further lambasting the criticism he has received from West Ham fans.
The 19-year-old defender, who can also operate in midfield, had his breakthrough season last term - starting 15 games, but he failed to start this campaign under new Hammers chief Manuel Pellgerini.
Rice is eligible to play for both England and the Republic of Ireland.
Various news outlets are reporting different contract offers.
But the Daily Mail have weighed in with a report claiming that the offer was as low as £12k-per-week. However, the club has the option to extend his deal another season.
The 19-year-old came up the ranks at the West Ham United academy and he broke into the first team set up last season when he ended up making 31 appearances for the club.
"As a team-mate, for me, he is one of those young players that you like to look after and help with all the information you can give him". The former Argentina worldwide believes the talented teenager has the potential to become one of West Ham's "greatest players".
"Declan is young, he still has room for improvement for sure, but you can see he has the right attitude and ability to be become one of the greatest players for West Ham", the Argentinian told the club's official website.
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