Such a reduction would be Sabadell's second in less than a year after recently cutting 1,817 jobs in Spain, where it employs a total of 14,648 people.
Union Comisiones Obreras (CCOO) said it saw no reason for a new round of layoffs at Sabadell, given "no economic, technical, productive or organisational causes".
Sabadell declined to comment.
Spanish and European banks are attempting to adapt to a customer shift towards online banking and cut costs, either by themselves or through tie-ups, as their overall profitability is also hit by rock-bottom interest rates.
Based on the outcome of previous negotiations, the actual number of job cuts could ultimately be lower.
The source told Reuters that 85% of the proposed staff reductions would mainly be in Sabadell's retail network. He also added that the bank expected to reach an agreement with unions towards the end of October.
In May, Sabadell said it expected additional cost savings and revenue growth from a push towards corporate and consumer lending in Spain to buoy profitability as part of its new three-year strategic plan.
The bank's return on equity (ROE), a measure of a bank's profitability, was 3.10% at the end of June compared to a current estimated cost of capital of above 9%.
Sabadell shares were down 1.45% to 0.61 euros at 1401 GMT.
The bank's failure to merge with bigger rival BBVA in November added pressure to pursue a more aggressive cost-cutting strategy as investors worried about its ability to handle an expected rise in bad loans alone.
Staff at Spanish banks have recently been holding protests against layoff plans.
BBVA and Caixabank recently agreed with unions to cut 2,935 and 6,452 employees, respectively.
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