Song has impressed since arriving from Barcelona and Allardyce has admitted that he would love to secure him on a permanent transfer.
However, the Hammers boss was cautious over his chances of actually being able to pull off the deal - suggesting that it will ultimately come down to Song's desire to play for them over any other club.
"It depends on whether Alex wants to stay," he said. "We want him to stay and I certainly want him to stay. But that lies with the financial side and the chairman with the negotiations.
"Whether that is financially feasible is another matter and if other clubs of a greater size entice him away. It will depend on if he feels comfortable enough to further his career at West Ham based on what we have done this year
"Performing the way we have done this year will of course help and if we can finish it off. There are many factors that have to be covered but if you ask me if I want him to stay – of course I do."
If West Ham were able to claim a European place their chances of landing Song would be greatly improved, with the Cameroon international likely to be keen on playing at the highest level available to him.
The Hammers are currently in seventh place in the Premier League table, but they are only three points away from the top-four and still harbour ambitions of sneaking into the Champions League spots.
If they are to do so, they will be relying on Song to continue his brilliant form. The experienced central-midfielder has dictated play for his side throughout the campaign and he sets the tempo for their matches.
If West Ham were able to secure his services on a permanent basis it would be a real statement of their intent, but if they fail to do so it will be a major disappointment for everyone at the club.