"I never look over my shoulder, never look behind. Somebody may be gaining on me. I run with blinders. I'll be prepared, whoever my opponents are," Specter said on CNN's "Late Edition."
Sen. Robert Menendez, D-N.J., the head of his party's campaign arm, said he has neither spoken with Matthews, a native Philadelphian, nor any intermediaries for him about a possible challenge to Specter.
"We'll see who decides to run. I haven't seen any firm announcement by anyone," Menendez said on the same program.
There was no immediate response from Matthews Sunday to a message left for him through an NBC spokeswoman.
The 62-year-old Matthews' contract with MSNBC expires in June.
He has worked in Democratic politics before, running unsuccessfully for a northeast Philadelphia congressional seat in 1974 and working for former President Jimmy Carter and former House Speaker Thomas P. "Tip" O'Neill Jr.
His brother, Jim Matthews, is on the Montgomery County Board of Commissioners in suburban Philadelphia.
Specter made it clear that he would vigorously defend his seat.
"Feeling good," quipped the Republican, who has survived bouts with a brain tumor and cancer while serving in the Senate. "Top of my game."
