The request was filed with the AU's legal affairs commission, the source, who is close to the pan-African body, told Anadolu Agency.
"Israel wants to join the list of countries with observer status at the AU at this time, when the voice of Africa has come to be increasingly heard," the diplomat, preferring anonymity, added.
In 1967, African governments suspended diplomatic relations with Israel in the wake of the 1967 war with Egypt, an AU founding member. The move was coupled with the withdrawal of several African ambassadors from the self-proclaimed Jewish state.
The Palestinians were granted observer status at a 1973 AU Summit and late Palestinian leader Yasser Arafat had been a frequent visitor to subsequent summits.
Palestinian President Mahmoud Abbas is attending the 22nd AU Summit, currently underway in Addis Ababa.
Egypt unilaterally opened diplomatic relations with Israel following the signing of the 1979 Camp David peace agreement.
The diplomatic source could not say how the AU would respond to Israel's request or when it would consider its application, sufficing to say: "The AU's decisions are principled."