The bidders could finalize terms in the next few weeks on the sale of two packages of assets worth about $8 billion in total, the people added.

Taiyo is in the frame to bag the European package, while Carlyle would take the U.S. assets, they said.

The two deals could clear the way to secure the $83 billion all-share merger of equals that Munich-based Linde and Danbury, Connecticut-based Praxair struck to create a global leader in gas distribution, with revenues of almost $29 billion and 88,000 staff.

Linde and Carlyle declined to comment, while Praxair and Taiyo were not immediately available for comment.

Linde and Praxair are pursuing talks to sell their European business lines to Japan's Taiyo Nippon Sanso for about $4.4 billion and have chosen Carlyle for the divestiture in the United States, potentially worth about $3.3 billion, the sources said.

They asked not to be identified as they were not authorized to speak publicly.

The sources added that both deals are not yet final and could still fall apart. Those who were outbid have been given the opportunity to improve their offers in case talks with Carlyle and Taiyo collapse, two sources said.

Price is not the only discussion point.

As Reuters reported earlier this month, the sellers specifically sought strategic buyers for Praxair's European operations to help win approval by antitrust regulators.

The European Commission, which decides on antitrust approval, typically prefers peer-to-peer mergers that create more globally competitive businesses.

A combined Linde and Praxair would have the size to overtake France's Air Liquide in the supply of gases such as oxygen and helium to industries worldwide.

(Additional reporting by Greg Roumeliotis, Ludwig Burger and Taiga Uranaka; Editing by Douglas Busvine and Louise Heavens)

By Harry Brumpton and Arno Schuetze