Both Saudi Oger and Saudi Binladin Group are understood to have submitted bids for the work, which is valued at SR500m ($133m).
A decision is expected within the next month.
Etisalat operates in Saudi Arabia under the brand name Mobily.
Both Saudi Binladin and Saudi Oger are also expected to be awarded contracts for the construction of a number of towers within King Abdullah Financial District in Riyadh in the coming weeks.
Saudi Oger is believed to have secured a SR1.4bn ($373m) design and build contract with the client, the Public Pensions Agency, for two towers, a hotel and an office block (MEED 15:09:08).
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