After Tottenham, Koeman's men face Arsenal, West Ham United and Norwich City, and the manager says his side could find themselves in the middle of the scrap to avoid relegation if they do not come out on the other side with a few wins.
"It's all about what happens in the next coming weeks I'm always positive (so) I think we will get good results in the next couple of weeks," Koeman told reporters on Thursday.
"But, if we don't get wins in the next couple of weeks, then we're close to the rest of the teams who maybe are now struggling against relegation.
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"I think to win the Premier League title, you don't need that number of points what normally you need – and maybe that's the same in the bottom of the league.
"Relegation (involves) more teams because we are so close to each other in the table. Everybody's worried, and that's in two weeks - and that's the Premier League.
"In two weeks you can be there, in whichever position you like to be but, if you don't win and you get three in a row that you lose, then it's a different world."
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by John O'Brien)
