The West Ham co-owner has given his verdict on the long-term futures of both his manager and star midfielder.
The answer in both situations, though, is that the club will review proceedings at the end of the current season.
Hammers boss Allardyce's contract at Upton Park expires this summer and Sullivan says he has a policy of only judging things at the end - or near the end - of the season.
That policy is as much for Allardyce's benefit as the club's, says Sullivan.
"We have a policy - and it’s as much for Sam as us - that we sit down at the end of the season, maybe a bit earlier if we’re safe, and judge things over an entire season," he told the London Evening Standard.
"We’ve always done it that way. Last year I was being asked at various times if Sam would be going but my answer was always that we’d look at it at the end of the campaign. We’re very loyal to our managers."
On Song, meanwhile, the West Ham co-owner believes he can become the best player at the club - but has once again reiterated that they will assess his long-term future at the end of the current campaign.
"First of all, I think Alex has been terrific but we haven’t seen the best of him yet," Sullivan said.
"He has admitted he needs more matches before he will be 100 per cent. I believe he could be the best player at the club. We have a season loan and there is no break clause.
"At the end of the season we will look at things. It might be he has higher aspirations than us but he may love it at West Ham. I know him and his wife love London."