Alonso has been linked with a move to Real Madrid this summer, while Mascherano is said to have caught the attention of Barcelona.
Perhaps more worrying, if true, is the claim that both players are hoping to leave Anfield during the close-season.
On Thursday, Alonso spurned the opportunity to commit his future to the Reds in an interview, while it was reported on Wednesday that Mascherano's agent had flown to Catalonia to speak to Barcelona officials.
It is said that Benitez hopes to meet with the duo's representatives to tell them that he wants their clients to honour their three-year deals at the Merseyside outfit.
However, while it is thought that the 49-year-old does not intend to sell Mascherano at any price, due to a breakdown in relations with Alonso, the Spain international may be allowed to join Los Blancos provided they make an offer close to €35.2 million (£30m).