They are bottom of the league, one point behind Worcester with only three games remaining.
But Cohen, 28, and Northampton chief executive Allan Robson have moved to dismiss reports the England World Cup winner could consider his future if Saints are relegated.
Cohen said: "I am incredibly proud to wear the shirt every time I pull it on, especially as Northampton is my home-town club.
"Whatever happens, I will still be here to help get Saints back up to the top of the Premiership."
And Robson added: "Ben's commitment to the Saints is not, and never has been, in doubt.
"His contract with us still has over a year to run, and any speculation about his future is total rubbish."