TDG has given Laxey Partners and Wincanton until 5pm on 20 June to make a firm offer for the company or walk away.
Wincanton entered the fray with a cash offer of 281.25p per share earlier this month (Wincanton joins the race to buy TDG), while Laxey Partners revealed its intentions in February (TDG's £222m takeover offer from Laxey Partners).
In a statement TDG said both parties had accepted the deadline.