Richard Taylor, the director of corporate affairs at Morrisons, told me that "no final decision has been made" on moving to selling groceries online yet.
He questioned whether introducing online shopping across the board would be fair on ordinary shoppers.
Online shopping is growing fast but is only five percent of the grocery market.
Morrisons suggest the higher costs of direct delivery mean the majority of customers end up subsidising the web savvy among us.
"Potentially customers who are shopping online [at competitors] are subsidising the ordinary shoppers - we don't think that's right," Mr Taylor said.
More top news
Noel Edmonds beat off competition from Ant and Dec to be voted Britain's favourite children's TV presenter.
A number of teenagers - including some who have never smoked - are experimenting with e-cigarettes, a study has found.
Singer Lil' Chris - who was found dead last week - suffered with depression and mental health issues for years, his family said.