Sissoko and Wijnaldum have both intimated that they could be interested in a move this summer, following the Tynesiders’ relegation to the Championship.
However, Benitez does not want to lose either of the pair - and he insists that they should stay to help the Magpies earn promotion.
“I understand they [Sissoko and Wijnaldum] need some time to analyse the situation and understand where they are, but they need to take their responsibility too and try to do their best to change the situation,” Benitez said.
“In this case, it would be to do well, get us promoted back to the Premier League and everyone will be happy.”
Sissoko has previously stated that he would like to play in the Champions League, while Wijnaldum has attracted the attention of a number of clubs.
Wijandlum has been linked with Tottenham Hotspur recently, but Newcastle are under no pressure to sell.
The Magpies promised Benitez that he would not have to offload any players he did not want to following their relegation.
Newcastle have sold Andros Townsend this summer, but they have moved quickly to replace the winger.
The North East side have brought in Dwight Gayle, Matz Sels and Matt Ritchie, and they are currently the heavy favourites to win the Championship.