The 53-year-old Portuguese has been reportedly linked with a move to Manchester United, but Syria wants Mourinho to coach a team currently ranked 123rd in the world.
"After a meeting including the president of the Syrian Football Association, the vice president and the general secretary, an official offer was agreed and made to the agency of Jose Mourinho to train the Syrian national team," said a statement from the Syrian Football Association, referring to the Portuguese coach's management team Gestifute.
"It is important for football in this country, at this time, to sign a world class coach to help us reach the World Cup for the first time in our history," added the statement. "We are open for negotiations to reach a deal between both parties."
Despite its lowly world ranking, Syria has been enjoying something of a footballing renaissance -- a feat all the more remarkable given the many millions that have fled the beleaguered nation.
The national team has just qualified for the third phase of the Asian qualifying competition, finishing Group E in second place behind Japan in March.
The letter to Gestifute, penned by Syrian FA general secretary Kouteiba al-Refaim -- and confirmed to CNN as veritable -- stresses these recent successes, before concluding with the valediction: "We send our best wishes and await your response to move forward with negotiations."
Between 2003 and 2012, Mourinho did not go a single calendar year without winning a trophy at the clubs he managed.
Syria, by contrast, has never qualified for the World Cup -- coming closest in 1986, only to be beaten at the final qualifying hurdle by Iraq.
'Why not buy Zidane as well'
Syria's move to employ Mourinho hasn't been overwhelmingly welcomed by some on social media.
One commented on Facebook that the Syrian FA were simply "delusional", saying: "Why not buy Zidane as well?"
Another made recourse to a famous Arabic saying:"If you have no self-respect, do whatever you please."
Gestifute -- founded by influential agent Jorges Mendes -- was not immediately for comment when contacted by CNN.
In December, Chelsea sacked Mourinho after an awful run of form left the English Premier League champion with no chance of retaining its title or qualifying for next season's Champions League tournament.