Evra made the claims on French television station Canal Plus after Saturday's Premier League clash at Anfield which ended in a 1-1 draw.
Uruguay striker Suarez has denied any wrongdoing, saying he is upset by the accusation, but Ferguson said Evra does not want to let the matter rest.
"We spoke to Patrice today and he was adamant he wanted to follow it on [complaint against Luis Suarez]," Ferguson was quoted as saying on United's website.
"It's not an easy one because everybody knows Manchester United and Liverpool have great responsibility. I thought Saturday was great in the stands and both sets of fans deserve praise for that. But Patrice feels very aggrieved by what was said to him and now it rests in the hands of the FA."
The Football Association has begun making enquiries after the allegations were brought to the attention of match referee Andre Marriner.
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