Rovers announced last month they were in negotiations with the Indian businessman, through his Bahrain-based investment firm Western Gulf Advisory, over a £300million deal, with Syed pledging up to £100million to spend on players.
But things have since gone quiet amid stories of unpaid debts and Allardyce has admitted he is not now expecting the deal to go through.
He said: "If it's happening, it's going to happen in the next week or two. But whether it does happen or not seems now doubtful, for whatever reason I don't know, I'm not privy to that information yet."
Allardyce also admitted the timing of the announcement had been unhelpful, coming as it did in the last month of the transfer window.
Blackburn were one of the lowest spenders this summer, with Hugo Fernandez their only permanent signing, and Allardyce was particularly disappointed to miss out on Bulgarian striker Ivelin Popov.
"The timing didn't help," said the Rovers boss. "People still felt we had a lot more money than we had coming up to the end of the window. It's been a distraction, I think."
Allardyce, meanwhile, did not rule himself out of the race to succeed England manager Fabio Capello once his contract runs out in 2012.
The 55-year-old was interviewed for the post following Sven-Goran Eriksson's departure in 2006 but was overlooked in favour of Steve McClaren.
Allardyce has made no secret of his interest in moving into international management, although he is thought to feel his chance of landing the England post may have gone.
When asked if he would consider applying for the job in two years' time, Allardyce simply said it was too soon to be thinking about it, adding: "I don't think past one week, and if I get past one month than I'm very, very lucky."
Capello confirmed he would not be seeking an extension to his contract following England's victory over Switzerland on Tuesday, which made it two wins from two in Euro 2012 qualifying and lifted the pressure on the Italian's shoulders.
Allardyce thinks Capello may have acted in the knowledge the Football Association would not have offered him a longer stay following England's disappointing World Cup showing in South Africa.
The Blackburn boss, meanwhile, hopes the Italian can follow in the footsteps of Bobby Robson, who led England to the semi-finals of the World Cup in 1990 when he already knew it would be his last tournament in charge.
Allardyce continued: "His contract runs out (in 2012) so I think he's probably pre-empted the fact that they probably wouldn't renew it before that and he can perhaps go out with a bang.
"I seem to remember the FA told Bobby Robson he wasn't getting his contract renewed and we had the best World Cup we've ever had since 1966."
And, even if Allardyce himself again misses out on the post, he is hoping it will be an English manager who succeeds Capello, as the FA have indicated will be the case.
He said: "I'd always like to see an Englishman succeed but the politics that are behind it is very, very difficult to overcome sometimes because it depends where you are and what you're doing at that particular time if you're English."