"I think the next few games are going to determine where our sort of ambitions are for the season. We're still in a relatively good position and want to go and finish the season strongly," Davis told the club's website.
"The last thing we want is for the season to just fizzle out, and there's still a prize in our sights there for us, if we go and put together a good run. That's the ambition and desire of the players to go and do that."
Southampton finished seventh last season and qualified for the early stages of the Europa League. They travel to the Britannia Stadium to face eighth-placed Stoke City on Saturday.
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(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Keith Weir)
