Southampton are not planning to do any more transfer business until they have appointed a new manager.
Adam Lallana and Luke Shaw have both been the subject of bids recently.
"It remains our preference not to partake in any transfers until the new manager is in place," the club said in a statement following Lambert's exit.
Liverpool have courted midfielder Lallana, 26, and last week submitted an offer of £25m for the Southampton captain, and also retain an interest in Croatia centre-back Dejan Lovren, 24.
Manchester United have held talks with the St Mary's side over a £27m deal for 18-year-old left-back Shaw.
Southampton's statement added: "We have received multiple offers for some of our players in the past weeks.
"We have no need to accept any offers. We are deep in the process of appointing a new manager who will continue to move our club forward."