The diplomats did not single out the United States as a potential target but told the British newspaper The Guardian Western targets in general would likely be marked for terrorist attacks.
The warning followed a car-bomb explosion Tuesday that destroyed about half of the French Embassy in Tripoli, Libya's capital. The attack, which French and Libyan officials labeled terrorism, was the most significant attack against a Western interest in Libya since the Sept., 11, 2012, attack on the U.S. diplomatic mission at Benghazi that killed U.S. Ambassador J. Christopher Stevens and three other Americans, The New York Times said.
The embassy explosion 7 a.m. Tuesday injured two French guards, one critically, but most employees had not yet arrived, Libyan and French officials said.
In Paris, President Francois Hollande said in a statement the bombing was "aimed, by way of France, at all the countries of the international community engaged in the struggle against terrorism."
French troops began military operations against Islamists in Mali, a former French colony, Jan. 11. Forces from African Union states were deployed shortly after.
Within a month, Islamist-held territory in northern Mali was retaken by the Malian military, with the French-led coalition's help.
The Islamist insurgent groups driven from northern Mali didn't just go away -- they fled across the Sahara to Libya, either through Algeria or Niger, both of which border Mali and Libya, the Western diplomats and Malian military officials told The Guardian.
This influx is fueling a growing Islamist insurgency in Libya, the diplomats said.
"There are established links between groups in both Mali and Libya -- we know there are established routes," a Western diplomat told the newspaper.
"There is an anxiety among the political class here that Mali is blowing back on them," the diplomat in Tripoli said.
"The armed groups we are fighting are fleeing to Libya," Malian Col. Keba Sangare, commander of Mali's army garrison in Timbuktu, told The Guardian.
"We have captured Libyans in this region, as well as Algerians, Nigerians, French and other European dual-nationals," Sangare said.
"If you squeeze a balloon in one part, it bulges out in another," Bill Lawrence, a regional director of the non-profit anti-conflict International Crisis Group political consultancy, told The Guardian.
"There's no question that the French actions in Mali had the effect of squeezing that balloon toward Algeria and Libya," he said.
2014: NFL Cheerleaders [PHOTOS]