Carroll scored in West Ham's 3-0 win against Jordan's old club Crystal Palace in January.
Dean Ashton celebrates scoring for West Ham United
Ashton, a former West Ham centre-forward himself, tweeted after England's 2-0 win against Lithuania on Sunday: "Still feel games like this are screaming out for @AndyTCarroll. Space wide. Time to deliver. Someone to attack it! No shame in that!"
But Jordan, the former Crystal Palace chairman, replied: "I think we should bring back Bob latchford #efc; Andy carroll - dean come on he has the grace and mobility of war horse".
And after Ashton sent Jordan a still of Carroll's acrobatic strike during West Ham's 3-0 win against Palace in January, the multimillionaire businessman was determined to have the last word.
Carroll has scored an impressive six goals in 15 Premier League outings this season, in what has been another injury-hit campaign for the 28-year-old.
His exploits, however, were again ignored by new England boss Gareth Southgate.
Carroll, who has scored twice in nine international appearances, last played for the Three Lions in November 2012, under Southgate's predecessor but one Roy Hodgson.
There could be hope yet for Carroll, however, with Jermain Defoe scoring on his return to the national team fold on Sunday, four years since his last cap.
The 34-year-old could be a teammate of Carroll's next season, having been strongly linked with a return to West Ham, the club at which he made his first professional appearance.
England's Jermain Defoe celebrates
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