Steve Tilson wants to remain manager of Lincoln and attempt to lead the club back into the Football League.
A 3-0 home defeat to Aldershot combined with Barnet's 1-0 home win over Port Vale on Saturday culminated in City being relegated from League Two along with Stockport.
"Of course I want to stay," said Tilson, who saw his side lose nine of their last 10 matches. "I'm as gutted as everyone is and I want to put it right.
"The summer is coming up and it will give us the opportunity to rebuild. We will have to have a think over the next two or three days about what we are going to do."