The Patriots are hot after one of the deepest positions in free agency, which is also one of their primary areas of need. The Pats showed interest in some of the best cornerbacks on the market yesterday during the opening of the 87-hour tampering window, inquiring about Sean Smith of the Miami Dolphins and Derek Cox of the Jacksonville Jaguars, along with Chris Gamble, who was released Friday by the Carolina Panthers. Smith and Cox can’t sign until their contracts expire when free agency officially begins on Tuesday at 4 p.m., but Gamble is free to sign now. One report indicated the Patriots were a favorite to land Smith, a second-round pick in 2009, but the word around the league is it’s still too early to describe anyone as a favorite to sign anywhere. Related to that, teams and agents were reluctant to divulge too much information because the NFL issued a strict memo Friday to remind them of the tampering rules. Violations call for $500,000 fines for all parties involved. The Patriots’ activity on the cornerback market makes sense. Alfonzo Dennard, Ras-I Dowling, Malcolm Williams and defensive back Devin McCourty are the only ones on the roster. Dennard, of course, will be sentenced next month for a third-degree felony assault of a police officer, so his status is up in the air. Plus, Aqib Talib and Kyle Arrington are free agents, so there are plenty of questions this offseason.