DUBAI, June 7 (Reuters) - Saudi Arabia is poised to price shares in the offering of its state oil giant Aramco at 27.25 Riyals a piece, people familiar with the matter told Reuters on Friday.

Aramco's book was covered 4-5 times at the bottom of the price range, one person said.

The Saudi government may sell up to a 0.7% stake in the world's top oil exporter. The banks on the deal had taken orders through Thursday and shares are expected to start trading next Sunday on Riyadh's Saudi Exchange.

The offering - codenamed Project Bond according to sources - has been in the works for months as a key step in drawing a broader range of investors after Aramco's record-breaking initial public offering (IPO) in 2019. The move will also further the kingdom's massive economic diversification programme.

The deal will be a test of interest in Saudi markets after lukewarm demand from international investors for the IPO amid concerns about a high valuation, Saudi government control and the energy transition away from hydrocarbons. ($1 = 3.7504 riyals) (Reporting by Maha El Dahan and Hadeel Al Sayegh; Writing by Nadine Awadalla; Editing by Michael Georgy and Muralikumar Anantharaman)