Analysts said Sainsbury could come back with an even higher bid, of perhaps 380p, later this week or early next week.
James Millar, chairman of Wm Low, repeated his advice to shareholders not to take any action on Sainsbury's pounds 210m offer until after the Tesco board meeting.
The Scottish supermarket chain had recommended a pounds 154m bid from Tesco before Sainsbury weighed in last Thursday.
For both groups the attraction of taking over Wm Low would be the creation of a significant presence in Scotland, where their market share is lower than south of the border, without going through a series of planning hearings.
Nick Bubb, retailing analyst at Morgan Stanley, said: 'Tesco would not ideally want to pay 350p, but it could afford it without much dilution. In strategic terms it is easy to justify.'
Wm Low shares closed at 323p on Friday.Reuse content