Fabio Borini’s agent admitted that Sunderland’s bid of around 18million euros is still on the table.
Kieran Agard's decision to join Bristol City ahead of Leeds has surprised Rotherham boss Steve Evans.
The goalkeeper, 32, put pen to paper after his deal expired at the end of the season.
Esson joined the Highland club from Hereford United in July 2008 following spells with Aberdeen and Shrewsbury Town.
He said: "I'm delighted as it was my preference to stay with the club and my family enjoy living in Inverness.
"The fact that it is a two-year contract gives me the security that I sought.
"The Caley Jags fans have been great for me and it's a relief to have my future sorted out so soon after the final game of the season.
"We suffered badly through an amazing glut of injuries this season but hopefully things will be much more positive in the new campaign."