Ministers have started consulting on a short-term visa scheme for lorry drivers after shortfalls reached “catastrophic” levels.
Officials at the Department for Transport (DfT) have asked the haulage industry to provide compelling evidence that visas would prevent gaps on supermarket shelves.
They reportedly believe this would break down Home Office opposition to relaxing immigration controls.
It comes after the Road Haulage Association warned the UK had a shortfall of 70,000 delivery drivers.
“Everyone involved is sworn to secrecy as the Home Office is taking a very hard line,” a source told The Telegraph.
“The Home Office has the final decision on this and the DfT knows it has a very tough sell, so need the very best evidence.”
Another insider claimed the government had had a “subtle change of heart” on the issue.
Transport minister Charlotte Vere reportedly accused the grocery sector of “crying wolf” over driver shortages as recently as last month.
On Thursday, following advice from hauliers and wholesalers, the government announced it would relax limits on how long HGV drivers could work per day.
The daily limit for time behind the wheel was raised from nine to 10 hours, with two 11-hour stints allowed every week.
Unite road transport officer Adrian Jones reacted furiously to proposals, claiming they would endanger drivers and “make an already difficult situation worse”.
A Home Office spokesman denied plans to introduce a short-term visa.
“Employers should invest in our domestic workforce instead of relying on labour from abroad,” he added.
The news comes after driver shortfalls left Sainsbury’s struggling to keep up with demand during the Euros.
Chief executive Simon Roberts admitted the supermarket had struggled to source salad packs, along with certain beer and soft drink brands, as families stayed home to watch the football.
Fellow Big 4 grocer Morrisons cancelled “ad-hoc” wholesale contracts for the same reason last month.