The Cottagers midfielder is out of contract this summer, and Celtic face competition from two of Europe's top clubs, a report claims.
Hyndman, 20, is said to have informed the Championship club of his wish to leave at the end of his contract this summer.
Fulham would be entitled to compensation for the USA international, which could equate to millions if he stays in England.
However, a move abroad would net the Cottagers just £200,000, and both AC Milan and Borussia Dortmund are understood to be keen, alongside Celtic.
Hyndman joined Fulham five years ago from FC Dallas and made his debut in the Londoners' first game back in the Championship - a 2-1 defeat to Ipswich Town in August 2014.
Injury cut short the Texan's 2014-15 campaign at just nine league appearances, but he returned to feature fairly regularly under Slavisa Jokanovic, who was appointed as head coach at the turn of the year.
Hyndman, who is of Portuguese descent, was capped by the USA in September 2014, though it remains his only appearance to date.