Workers have been unhappy since two external companies took over production for the BBC's flagship religious programme last month.
Their concerns will be raised on Monday in a meeting between the show's new co-producers and the media union Bectu.
Head of Bectu, Gerry Morrissey, told the Sunday Times: "Strike action will be very much on the agenda."
In a deal worth £12 million and spanning the next three years, independent companies Avanti Media and Nine Lives Media took over producing Songs of Praise.
Staff are due to transfer to Cardiff-based Avanti Media in June however they fear missing out on a pay rise expected for BBC workers.
There is also concern they will get smaller pensions.
Song of Praise, whose presenters include Premier Christian Radio host Pam Rhodes, has been a familiar feature on television schedules since it was first broadcast in 1961.
Former Conservative minister and occasional Songs of Praise presenter, Ann Widdecombe told the Sunday Times that the show was "probably the last bastion of Christianity on television."
She added: "I think it can survive but it needs to be properly handled."
The newspaper quoted Avanti Media as saying the programme would continue on air as scheduled.
The BBC told the Sunday Times: "We haven't agreed a pay deal for BBC staff or changes to terms and conditions with the union yet and have not been informed of any dispute."