Sky Blues owners SISU are in talks to play their home matches at the Sixfields Stadium while their new ground is being constructed.
Sillett has threatened to step down from his post as life president if the move goes ahead, according to The Sun.
Coventry fans have also expressed opposition to the groundshare, with many staunchly against the team leaving its home city.
"This is a terrible day for Coventry," said Malcolm Clarke, chair of the Football Supporters' Federation. "To see your club ripped from its community is one of the hardest things for a fan.
"Although 34 miles is only an hour's drive, there's a gap of a million miles between the views of supporters and of venture capitalists SISU."
Coventry's proposed groundshare with Northampton is expected to last at least three years with the deal goes through.