Victory at bitter rivals Burnley on Sunday saw Rovers pass the 40-point barrier, leaving them 14 clear of the bottom three.
With six matches to play, it is almost inconceivable Blackburn will be dragged into any kind of late dogfight, which is why Allardyce can now turn his attention to strengthening his squad.
The Blackburn manager's main priority, aside from securing another striker, is to see midfielder Pedersen put pen to paper on a fresh deal.
The Norwegian, who has spent the last six years at Blackburn, has so far shown little indication of committing himself, but Allardyce wants an end to the matter - and fast.
"There's a contract we want Morten to sign so I hope his and the chairman's representatives can secure a deal tomorrow. That would not be soon enough for me," Allardyce said.
"Morten has suggested he wants to stay and, if that's the case, get it done and dusted and don't leave the door ajar for somebody to step in and make it impossible for us to sign him from there on."
Allardyce admits he does not like "situations lingering", especially as Pedersen remains vulnerable to another club offering a pre-contract agreement.
"I don't have any doubts (he will sign), it's just that the two parties need to come together and thrash it out," Allardyce added.
"So whether we go to him, he comes to us or there's an exchange of emails, I'm not bothered how it's done, just as long as it's done as quickly as possible, and it needs to be done very, very quickly.
"Because we're now in a comfortable position, we can't afford to let these things pass by, in particular when there's still a chance for anybody outside of this league to knock on his door and say 'Sign this contract.'
"He could sign it, and he doesn't even have to let us know, and then lo and behold, all of a sudden, it's too late."
Allardyce's immediate concern is Saturday's trip to Portsmouth, who could be relegated if they lose and Hull and West Ham win.
The Rovers biss feels Pompey's demise has been of their own making given the financial mismanagement which that has taken place.
"From the very start it looked like life was going to be very difficult for (former manager) Paul Hart," Allardyce said.
"I thought he did a fabulous job in that he rescued the situation from the financial troubles they were in.
"He and (chief executive) Peter Storrie put a team together, although it was pretty much thrown together, and there seemed to be a little turn around in fortunes.
"But they had a dip, changed manager and then the financial crisis hit, and no matter how hard everybody tried to find and secure a new owner, it just wasn't the case.
"It has ended up with where they are now, in administration, and nobody wants to see that.
"But unfortunately, the millions and millions of pounds they have had over the years has not been put to good use.
"It has thrown them into complete and utter chaos financially, and they've spent far more than they could afford to."
With virtually a fully-fit squad to take to Fratton Park, Allardyce is looking to secure three consecutive league wins for the first time this season.
Captain Ryan Nelsen and goalkeeper Paul Robinson are ready to make comebacks after missing the last five and three games respectively with knee and calf injuries.