The 73-year-old musician and the journalist, 43, had been dating since earlier this year (16), after Roger's separation from his fourth wife Laurie Durning and Rula's split from her entrepreneur husband Arthur Altschul Jr.
The pair reportedly bonded over their concern for the rights of the Palestinian people and condemnation of their treatment by the Israeli government.
According to a source close to the couple however, their whirlwind romance has come to an end.
"It was over as quickly as it began - while they agreed on many issues, they couldn't find common ground on others," the insider told editors at the New York Post's Page Six gossip column. "Plus, their families didn't get along."
In addition to her journalism career Rula, who holds Israeli and Italian citizenship, has worked as a foreign policy analyst for U.S. TV network MSNBC and released her debut novel in 2013.
She first met Roger when they were introduced by their respective spouses.
Their partners reportedly found their relationship difficult to come to terms with as both couples had socialised together.
"It was very weird for their former spouses, who introduced them," the source claimed. "Rula had asked to meet Roger because he's a vocal activist for Palestine. The two former couples have had dinner together many times. They were all friends."