The 105km-long offshore pipeline section will be built at a maximum depth of 820m.
The first pre-qualification includes engineering, procurement, construction and installation (EPCI) works for the offshore pipeline section between the coastlines of Albania and southern Italy.
The EPCI scope of work includes associated landfall civil works in both Albania and Italy, and survey, seabed and pre-commissioning activities.
The second pre-qualification process involves offshore line pipes and coating.
Invitations to tender (ITT) will be issued by May 2015.
TAP procurement director Knut Steinar Kvindesland said: "I am delighted to invite companies – including those from TAP’s host countries – to submit expressions of interest in line with the pre-qualification documentation now available on TED.
"The selection of potential suppliers will remain rigorous, with particular emphasis on meeting Health, Safety and Environment standards and a proven commitment to TAP’s zero harm policy."
TAP will transport natural gas from the giant Shah Deniz II field in Azerbaijan to Europe.
The 870km-long pipeline will connect with the Trans Anatolian Pipeline (Tanap) near the Turkish-Greek border at Kipoi, cross Greece and Albania and the Adriatic Sea, come ashore in Southern Italy.
BP holds 20% share in TAP, while the other partners include Socar (20%), Statoil (20%), Fluxys (19%), Enagás (16%) and Axpo (5%).
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