The practice - pensions clawback - has angered members of Barclays' pounds 10bn pension fund who find they can lose up to pounds 30 a week from their pension income. The fund has a surplus of more than pounds 2bn.
Following a meeting with the Barclays finance union, Unifi, the Barclays pensions director, Martin Hodgkinson, said he would take the issue to a meeting of the board of directors in August.
Unions have opposed the practice, which appears to undermine the principle that occupational pensions should be a "second tier" above the basic state pension.
Under pensions clawback, employers can reduce an employee's income from an occupational pension by an amount up to the value of the basic state pension, now pounds 64.70 a week. Up to 2.5 million pensioners in the UK are affected by clawback, which is used by 44 per cent of employers.
In some schemes, a pensioner paid an occupational pension worth pounds 100 a week could see it reduced to the level of the basic state pension - in effect shrinking the value of the pension rights to nothing.
Nearly 100 MPs have backed a campaign to have the practice abolished as part of the Government's review of pensions.