The boss revealed that discussions with the Reds have been held but no agreement could be reached, before fiercely denying an interest in the available Bulgarian
New Anfield boss Brendan Rodgers recently revealed at a press conference that the forward could be allowed to leave on loan, with former club Newcastle United having already had an offer rejected.
And Allardyce confirmed that despite discussions between the two sides taking place, no agreement was found, leaving the former Bolton manager to move on to other targets.
He told Sky Sports News: "I think that we're not in a situation where we can secure a deal with Andy or Liverpool at the moment.
"We talked to them, we had some negotiation. But at the moment there is nothing progressing forward on Andy coming to West Ham.
"Andy is yet to make his mind up where his future lies and the negotiation with Liverpool hasn't been a situation where we've been able to agree.
"We'll just leave it as it is and move on with other players, as we have been doing on a daily basis through the summer."
Allardyce was considerably more assertive regarding rumours linking the Upton Park outfit with Berbatov, claiming the story is simply guesswork and that he has not spoken with Manchester United manager Sir Alex Ferguson.
He continued: "That's pure speculation in the media. I haven't had any contact with Sir Alex.
"There was a statement from Dimitar saying he's available for €6.3 million (£5m). Everybody knows we're looking for a striker so they say we're in for him, but I've not had any conversations with Sir Alex."