The Spaniard, who had thought he may lose his job, may now be dictating transfer policy.
Lopetegui admitted that he and Sullivan are discussing moves they can make in the January window.
“The talks I have with David I am not going to tell you, but we talk a lot about the team, about the squad and about the next challenge — but the only focus we have now is Southampton,” said manager Lopetegui to reporters.
“There is no more space in my mind now, only this. The only truth I believe is to be focused on the next match. After, we will see what happens.”
“Any attacking player is much better if his focus is on his defensive work,’ added Lopetegui on forward Mohammed Kudus.
“Football is about being focused always and a collective game.
“It was a pity he was out for five matches and it’s not easy to recover the rhythm in the Premier League.
“He is doing that and we are happy for him. He is doing well and is helping the team.”