Terry Harris/Rex Features
HP workers at the Department of Work and Pensions, the MoD and General Motors had voted to go on strike for four more days in two 48 hour stoppages. The dispute involves pay and pensions.
A source said the workers are "going to be quite happy" with the offer.
If a compromise is reached HP in this case will join Siemens and Fujitsu in avoiding strike action.
Siemens workers at the BBC recently accepted a pay offer and Unite members at Fujitsu have voted in favour of accepting an offer made by the employer through ACAS.
Also workers at HP and Unite members at HP CDS recently averted planned strike action over job transfers.