The Bank of England is expected to keep interest rates at their historic low of 0.5% on Thursday.
But it may announce an extension of its quantitative easing scheme under which it prints money to buy bonds in order to stimulate the economy.
At the moment it plans to spend £125bn, but it can increase that by £25bn without asking the Treasury.
At the current rate of spending, the £125bn will all have been spent in the next two weeks.
Taking on the extra £25bn would allow the Bank's Monetary Policy Committee (MPC) to see the next set of quarterly economic forecasts before it decides whether to ask the Treasury to extend the scheme further.
Investec economist Philip Shaw said he expected that the Bank would spend the extra £25bn - as well as asking permission to print more money.
But he said it was "early days" to judge whether quantitative easing was proving effective.
"We are waiting for the banks to start lending but there are very few signs that has happened so far."
At its last meeting, the MPC noted there had been encouraging news on the economy.
"Overall, the risk of a continued sharp contraction on output in the near term had receded somewhat," the minutes from the June meeting said.
However, the committee added that there was not enough evidence to suggest that the medium-term outlook for the economy had changed significantly since the Bank's last Inflation Report in May.
While survey evidence from the likes of the British Chambers of Commerce suggests that economic conditions may be improving, economic data has showed continuing declines.
Since the MPC last met, the contraction in the UK economy during the first three months of the year has been raised to 2.4% from 1.9%, a decline not exceeded for 51 years.
Also, UK unemployment rose to 2.261 million in the three months to April, the highest since November 1996, while industrial output fell by an unexpectedly large amount in May following a rise in April.