The MPC will publish its regular decision on borrowing costs at midday.
Mr Posen, interviewed on the Today programme on Radio 4, said rates may not rise until next year.
"I think they are not going to vote for a rate hike at this time and probably not until at least November and maybe not even until 2018", he said.
The Bank last changed interest rates in August last year when it cut its bank rate from 0.5% to 0.25% in the immediate aftermath of the UK's referendum vote to leave the European Union.
Mr Posen was asked why the Bank should not raise rates now, given the worrying rise in consumer borrowing and the past year's rise in inflation to 2.6%.
He said the Bank's role was to judge where inflation might be in two to three years time - and he said that the Bank's current forecast was "too high".
"It is pretty clear the economy is slowing... it's a credit-fuelled expansion and so it's likely to come to an end soon," Mr Posen said.
"There's no good reason for the pound to appreciate further right now, particularly against the euro," he added.
He also disagreed with the widespread view that the Bank's policy of low interest rates had stoked up excessive consumer borrowing and that this problem should be dealt with by raising rates.
"The big lesson of the financial crisis is that the one interest rate the central bank controls doesn't have that much implication for the whole range of financial products and borrowings that exist in a modern economy," he said.
"We were unable to stop [the crisis] solely by moving down the interest rate and we've been unable to reflate the economy just by moving the bank's interest rate also," he added.
Instead, he argued, the Bank's Financial Policy Committee (FPC) should use its powers to limit the lending of commercial banks where it thought this had got out of hand.
In recent months members of the MPC, including the Bank Governor Mark Carney, have differed publicly over whether or not rates should rise soon.
For instance, in June Mr Carney said the time was not right for a rate rise.
The next day the Bank's chief economist, Andy Haldane, said he favoured increasing the cost of borrowing later this year.
Then a week later the Bank's deputy governor, Sir Jon Cunliffe, publicly suggested that now was not in fact the right time for such a move.
That flurry of debate reflected the unusually divided vote at the last MPC meeting in June, when its eight members voted by only 5-3 to keep rates at their current level.
Mr Posen, who was an MPC member from 2009 to 2012, said there was nothing wrong with close votes as it indicated that active debate was taking place within the committee.
And he said there was "no mistaking the fact" that following Brexit, the UK economy would suffer a shock and that in two years' time it would be in "much worse shape" than it is now, with higher inflation.

The Scotland full-back, 30, joined the Warriors in 2009 from London Welsh and has since played more than 100 games.
"I've witnessed huge growth at the club and we're now selling out Scotstoun for the majority of our home games and it's a great place to play rugby," he said.
Meanwhile, 24-year-old full-back Glenn Bryce, who has made 13 appearances, will join Edinburgh in the summer.
He joins team-mate Duncan Weir in switching to the Warriors' Scottish rivals.
Bryce told the Warriors website: "It was a really hard decision to leave Glasgow but I'm hoping to kick on at Edinburgh and play as regularly as possible next season.
"Getting involved during the Rugby World Cup period for Glasgow was a high for me. I've loved my time at the club."
Murchie captained Warriors to a 12-6 win over Leinster on Friday as the defending champions continued their push for a Pro12 play-off place.
He joins Jonny Gray, Finn Russell, Pat MacArthur, Fraser Brown, Alex Allan, Sila Puafisi, Ali Price, Ryan Wilson, Rob Harley and Chris Fusaro in committing his future to Gregor Townsend's team.
"Peter has made a huge contribution to the club over the last seven years, so it's great news that he's staying with us," said the head coach.
"He sets the standard for the squad in how to conduct yourself as a professional and works very hard to improve as a rugby player."
A former member of the Monetary Policy Committee, Adam Posen, has predicted that the Bank of England will not change interest rates this month.
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Peter Murchie has signed a new one-year contract with Glasgow Warriors, keeping him at Scotstoun until May 2017.