The Hammers secured a coup on the final day of the summer transfer window when signing the England international on loan from Liverpool for the duration of the 2012-13 campaign.
Carroll has been restricted to just 11 Premier League starts due to injury, but was fit again at the end of January and has made a big impact on his return to the first team, scoring in an important home win over Swansea on February 2.
West Ham are reported to have an option to purchase Carroll for £17 million but Allardyce says all parties concerned will look at the situation come the end of the season.
He told Yahoo!-Eurosport: "I think it depends where we finish, it depends what Andy feels, what Andy thinks, what the owners feel.
"There's a lot of things that would have to be discussed before we decided on whether we will or we won't."
Allardyce said of the striker's recent return to action: "His frustration and our frustration has been those injury problems and we have all seen what he is capable of.
"But there is still a lot more to come. Whatever the West Ham fans have seen, they haven't seen the best of Andy Carroll yet.
"I hope I can extract that out of him between now and the end of the season and I think if Andy stays fit, people will see an even better Andy Carroll than they have seen already."
Sam Allardyce was speaking to Yahoo!'s 'The Dugout' through its partnership with the League Managers Association