Ralph Hasenhuttl hopes Danny Ings will decide to take up Southampton's offer of a lucrative new deal, but maintains the club are 'not addicted to one player'.
Saints are said to be willing to make the England forward the highest-paid member of their squad in order to secure his long-term future.
The former Liverpool man, who completed a permanent switch to St Mary's in the summer of 2019 following a season on loan there, is an integral part of Hasenhuttl's sixth-placed side.
And Ings marked his return from a knee problem by coming off the bench to score a late penalty in the 2-1 win at Brighton on Monday night.
Hasenhuttl said: "Danny has come from a bigger club and he knows what he has, now he is here.
"I see in every training session how much he enjoys playing here, but he also sees that there are now more and more players committing to our way and signing new contracts.
"As I said, who wants to be part of this, is invited to come.
"I think the offer we made him is a fantastic one and, in my opinion, we showed him how much we want him to stay here and the rest is on him.
"Now he has to take the responsibility for this and we will have to live with it too.
"We are not addicted to one player only and we must always have a squad that can replace anybody.
"We have a good core now after extending contracts and we have a few players negotiating.
"We are building the future at the moment and those who want to come with us are heartily invited."
Hasenhuttl expecting tough game against Blades
On Sunday, Southampton host bottom club Sheffield United, who have only picked up one point so far from 11 games.
Hasenhuttl is determined to make sure the Blades' revival does not begin against his side.
"It is for us to not let them start winning this weekend," he said.
"The second year (in the Premier League) is always tough. There is a long way to go and they have shown last season they can be a good side.
"We will prepare for the best possible Sheffield side we can.
"The message from my team will be that we have a tough game.
"They have struggled at the beginning, but they have shown they can play well."