The 24-year-old has spent the season on loan with the Hammers after being deemed surplus to requirements at Anfield and scored seven goals in 24 games.
Manager Sam Allardyce has made it clear of his desire to sign Carroll on a permanent basis, but feared the club would be unable to meet his wage demands.
However, it would now appear just a case of convincing Carroll his future lies at Upton Park.
The former Newcastle striker said earlier this week: “I have had a great season here at West Ham. Everyone has been so welcoming to me. This is a great club.”
One player definitely joining West Ham is Romania captain Razvan Rat, 31, who has penned a one-year deal, after his contract with Shakhtar Donetsk expired.
However, it would appear Rat will not be playing in the same team as Carlton Cole next season, after the striker wrote on Twitter: “Life is filled with ups & downs today is a down but I'll be back! Carlton Cole/CFC as I have been called has left the building.”