Roberto Martinez was sacked by the Merseyside club on Thursday after three years in charge and Koeman has since been linked with the job.
The Dutch boss has a year left on his contract after taking over at Southampton in August 2014 and told the assembled media at his Friday press conference that he has no interest in leaving just yet.
Asked if his future was staying at Southampton he answered: "Yes
I did not expect this question
After this morning, I was surprised
"(I can tell you) nothing, because I am the manager of Southampton.
"Everybody knows I have one year left on my contract and we will sit together and analyse this season and we will talk about the future and that is what the news is today."
Koeman will meet with Les Reed, the director of football at Southampton, after the season finishes on Sunday to discuss his contract extension but the Saints boss is pleased with the progress of the club.
A win over Crystal Palace on the last day of the Premier League season will keep them in with a chance of Europa League qualification for next season.
He said: "What is good is that the club are happy with the work, together with the technical staff and the players, that we have done
"There is a very good understanding between the manager and the players and that is good because it is important to continue.
"So let's do our job this weekend and there is time enough before I go on holiday to have a talk about the future of the club.
"Everything can happen very fast and that is no problem."
Source : PA
Source: PA