The Liverpool star managed a hattrick for Brazil in a 7-1 win over Haiti this week.
The Sunderland striker says his superb season was down to Allardyce's willingness to play him in his preferred position.
The Sunderland manager believes the striker, who has been awarded new terms by the Black Cats, is one of the best strikers in England since 1992.
Coutinho netted a hat-trick for Brazil in the Copa America.
Spurs ended up finishing the Premier League in third position.
Sunderland are expected to back Sam Allardyce with funds during the summer transfer window.
Everton are reportedly targeting the Burnley and Brighton and Hove Albion defenders this summer.
Tottenham Hotspur striker Harry Kane is expected to lead the line for England at Euro 2016.
The Paraguayan has found his form in his homeland.
Liverpool will announce their released and retained list tomorrow.