Drivers at other companies are voting in a consultative ballot on proposals tabled following the Acas talks, with a recommendation to reject.
Unite said while progress had been made in the talks on health, safety and training, representatives at a special oil trades conference recommended rejection, following employers' "failure" to give sufficient guarantees on maintaining standards, security of employment, pensions and sub-contracting.
The result of the consultative ballot involving tankers drivers working for other firms including Wincanton, DHL, BP, and Norbert Dentressangle, will be announced on Friday, when Unite will disclose the next steps in its campaign.
The vote in favour of action short of a strike demonstrates that deep concerns still remain in an increasingly insecure and unstable industry.
Tanker drivers face a daily race to the bottom where contracts are chopped and changed. It is in everyone's interest to bring order to the chaos gripping a vital industry through the introduction of industry wide minimum standards.
– Unite assistant general secretary, Diana Holland
Talks aimed at resolving a dispute involving fuel tanker drivers will resume on April 23 in a bid to avert strikes.
Leaders of the Unite union will meet officials from six distribution companies under the chairmanship of the conciliation service Acas.
Unite has been given an extension to April 24 before it has to make a decision about calling industrial action.
The two sides have already held six days of talks, but tanker drivers' representatives overwhelmingly turned down a proposed agreement last week despite progress being made on some of the issues involved in the row.