The 29-year-old has started just three times since Steve McClaren took charge of the England team, and his absence from the Euro 2008 qualifier against Estonia last month is reported to have brought things to a head.
With Rio Ferdinand and Jonathan Woodgate sidelined, Carragher was expected to feature alongside John Terry, particularly having helped Liverpool reach the Champions League final with a string of wholehearted displays.
But McClaren opted for Tottenham's Ledley King in central defence and named Carragher among his substitutes.
A 'source close to Carragher' is quoted as saying in the Mail on Sunday: "Jamie does not want to sound like a big-time Charlie.
"He just feels that at this stage in his career it would be better if he concentrated his efforts on helping Liverpool become the No 1 team in England again.
"He has always regarded it as a tremendous honour to represent his country...but things have to end some time and he thinks this might be a good time to bow out."
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