Despite the protracted negotiations, Allardyce said: "It is not as quiet as everyone thinks it is because [the deal] is very close to being clinched."
The former Newcastle boss added the new owners would be healthy for the club.
Rovers chairman John Williams said in October that both parties were "hopeful" the deal would be secured in November after talks with Indian businessman Ahsan Ali Syed's company began in August.
"I spoke to the chairman this morning and the club expects to make an announcement very shortly," Allardyce added.
Following the initial talks in the summer, Allardyce was promised a £100m transfer kitty, although Venky's - short for Venkateshwara Hatcheries Group - have since revealed few details on any potential investment.
Allardyce, who took over the helm in December 2008 after a 24-match spell at Newcastle, is happy with the proposed takeover of the club, which has been run by the Jack Walker Trust since the death of its former benefactor a decade ago.
"It would be very disappointing if it wasn't somebody that wanted to take over the club and try to improve it as quickly as possible," he said.
What do you make of Blackburn's proposed takeover? "The best way to improve a football club in the early stages is the first-team results. We all know we have been short of a bit of investment in the last few years.
"Since the trust has tried to sell the club they haven't been willing to fund the sort of transfers needed to keep the club improving. That's put it in danger of being in the throes of selling your best players and threatened with relegation."
If the deal is successful, it would make Rovers the first Indian-owned Premier League club.
According to its website Venky's, formerly known as Western Hatcheries Ltd, was established in 1976, mainly to produce chicks for the poultry markets of north India.
The VH Group company was founded in 1971 and has diversified into manufacturing nutritional health products for humans, pet food and other healthcare products.
The Jack Walker Trust put Blackburn up for sale two years ago in the hope of attracting buyers willing to invest, but Venky's is the first company to have satisfied club chiefs about their future intentions.
Blackburn are 14th in the Premier League just two points above the relegation places having picked up four victories in 13 games.