The 31-year-old back-row forward has been linked with a return to his first club Montpellier.
"I don't think Northampton has ever been a selling club," said Mallinder.
"We want to keep all our good players. Louis signed a three-year contract, he has just finished the first year, and he has no get-out clause."
He added: "There is no reason why Louis should be anywhere else."
Speaking after Northampton's narrow final-day Premiership win against Harlequins, Mallinder admitted: "He was immense. You need all your big players playing because the competition is tough now.
"The other teams are good, they have quality players as well, so we need all the good players we can get. We have always wanted to go into the market and bring good players to Northampton."
Picamoles, who joined Saints from Top 14 side Toulouse last summer, has been hugely influential for Saints this season, earning him one of the five nominations for the Rugby Players' Association player of the year award.
But reports have suggested that fellow Top 14 side Montpellier, owned by billionaire Mohed Altrad, want to give him a central contract with the French Rugby Federation (FFR).
Montpellier, where Picamoles played from 2004 to 2009, are reportedly preparing a seven-figure sum to try to buy the number eight out of the remaining two years of his contract and offer him a return to France.
Saints' victory was not enough to secure an automatic place in the European Champions Cup next season as Quins' losing bonus point ensured them sixth place.
After finishing seventh, Northampton, Premiership champions in 2014, now have to hope that Gloucester lose the Challenge Cup final against Stade Francais at Murrayfield on Friday if they are to claim a play-off spot for another chance to play in European club rugby's top competition.
Northampton have "no reason" to have to sell France international Louis Picamoles, says Saints director of rugby Jim Mallinder.