Sky Sources understand that the FA are surprised by the decision - which was made by an Independent Regulatory Commission - and will await the written reasons before considering an appeal.
Ianni admitted an FA charge of "improper conduct" after his celebration in front of the opposition bench sparked an altercation with United manager Jose Mourinho at Stamford Bridge earlier this month.
Despite Mourinho being cleared this week, the FA could launch an appeal against the decision.
"Written reasons for the decision of the Independent Regulatory Commission will be published in due course".
Wayne Rooney, who became United's record goalscorer before leaving in 2017, believes it is down to the team's highly-paid stars to play with more pride and passion regardless of their issues with Mourinho.
Following the game, Mourinho raised his little finger towards a TV camera and appeared to say something in Portuguese.
In their original statement on October 16, the FA said: "It is alleged that his language at the end of the fixture, as captured by the broadcast footage, was abusive and/or insulting and/or improper".
Manchester United haven't won the Premier League title since 2013 when Sir Alex Ferguson was still in charge, although Mourinho has won the top-flight title on three occasions.
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