Carroll has struggled with injuries during his time at West Ham, although he is now fully fit and is firing in the goals.
Shearer, who managed Carroll for a brief period in 2009, seems to rate the former Liverpool striker, but he has highlighted his injury issues.
“I know Carroll reasonably well and there is no doubting he has ability,” the former Newcastle striker has written in The Sun. “The problem is we only seem to talk about it every now and then before he gets injured once again.
“I want to be talking about Carroll having a great 18 months — not a great game once in a while. That is down to him.”
Carroll has scored three goals and created five chances in 12 Premier League appearances so far this season.
The England international has a pass accuracy of 63% and a shot accuracy of 61%, and has won 42 headers, two dribbles and one tackle.
West Ham are sixth in the Premier League table at the moment with 32 points from 20 matches.
The Hammers are just four points behind Tottenham Hotspur, who are currently fourth in the standings and occupy the final Champions League spot.