The 33-year-old striker has struggled with injuries this term but showed his value with a vital equaliser in the recent win over Brighton and started his first match in seven months as Saints beat Hartlepool on Monday.
Connolly will be out of contract in the summer and nothing has been discussed regarding a new deal.
But he told the Echo: "I still feel young and I'll be one of the fittest around. I've got so much in me.
"It's up to the club, I don't know what they're thinking.
"For example, if I hadn't come on (against Brighton), no-one would have been saying anything about me, and I'd be in the same position."
Source: PA
Source: PA