The former Newcastle United forward has not played for the Three Lions since October 2012, with injuries derailing his progress.
He won the last of his nine caps under former boss Roy Hodgson but he is now pushing for a recall under Gareth Southgate. After returning to the West Ham fold this season, Carroll has impressed under Slaven Bilic and Cresswell believes his aerial threat could be crucial in Russia.
He told Press Association Sport: "Of course he can. Everyone knows what Andy is capable of, especially in the air, and you could say it's a different dimension and that different way of playing.
"If Andy stays fit between now and the end of the season, there is no reason why he can't be in contention.
"Everyone wants to be pushing for that World Cup spot and all you can do it keep playing your best week in, week out and hope to make that plane."