The discussions, held at the Four Seasons hotel in the city's upscale 8th arrondissement, were "constructive", according to two people with knowledge of the meeting.
Existing rules mean that a US company can forgo its domestic tax status through a deal that transfers more than 20 per cent of its shares to foreign owners.
A tax inversion by Walgreens would be likely to face strong political resistance in the US, where the practice has become increasingly popular during the past two years, particularly in the pharmaceutical sector.
As well as pushing the executives to consider an inversion, the shareholder group told Messrs Wasson and Pessina that they wanted to see a greater role for Boots' management team in running the merged business.
Read MoreUS acquirers cut taxes by relocating to Europe after mergers
Illinois-based Walgreens acquired 45 per cent of Boots for $6.5bn in cash and shares in 2012, with an option to buy the remaining 55 per cent next year for $9.5bn. The combined business would have sales of $110bn, based on 2013 figures.
Alliance Boots has been criticised by tax protest groups, including UK Uncut, over claims that it had reduced its tax bill since being taken private by Mr Pessina and private equity group Kohlberg Kravis Roberts in a £12bn deal in 2007.
Walgreens and Alliance Boots both declined to comment.
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