Last week Salerno vetoed the idea, opting instead to continue with litigation, sources told Reuters.
Salerno and Phillips declined to comment. In a statement, Viacom did not confirm or deny it received such an offer from Redstone. But did say it would be wrong to suggest such a meeting could "actually assess" Redstone's capacity.
Salerno has sent a number of letters to Redstone over the past several weeks requesting a meeting with him to discuss his views of the business, and to go over the rationale for Dauman's planned stake sale of Viacom's Paramount movie studio.
"We are quite concerned that your voice — and views — are not being heard," Salerno wrote in a June 14 letter, made public by Viacom.
The fact that the Viacom board rejected Redstone's offer of a meeting with Phillips showed claims by Viacom executives and Salerno that they are being blocked from meeting with Redstone are "fiction," said Mike Lawrence, a spokesman for Redstone, in a statement.
"Fred Salerno, Philippe Dauman, and (Viacom board member) George Abrams have repeatedly told the courts that the Viacom board is being blocked from meeting with Sumner, leaving them no choice but to pursue claims," Lawrence said in the statement. "That fiction has been shattered."
Viacom called those statements both inaccurate and incomplete.
"The one fact not in question is that an examination to assess Mr. Redstone's capacity and undue influence needs to happen," the company said in a statement.
For investors, the impasse could mark the beginning of a long legal battle that will prolong the uncertainty over the future of Viacom. The company's shares closed down 5.1 percent on Monday, in a broadly lower market.
Redstone's privately held movie holding company, National Amusements Inc, owns 80 percent of the voting shares of Viacom as well as CBS. On June 16, when National Amusements moved to oust the five directors from the board, investors told Reuters they hoped a change in management or a merger between CBS and Viacom could be on the horizon .
On the same day, National Amusements asked a Delaware court to affirm the changes, while Salerno shot back with his own suit seeking to block the move, calling it "invalid" and the result of Redstone's daughter Shari Redstone manipulating her father.
A Delaware judge said last week that he would schedule a hearing in July in a case about whether National Amusements' move was valid.