The Patriots have their hands in the honey jar. Former LSU cornerback Tyrann Mathieu will make a formal visit to Gillette Stadium next Friday, according to a source, so the Pats will get an up-close look at one of the most high-profile athletes in the upcoming draft. Mathieu was an electric playmaker and Heisman Trophy finalist for the 2011 SEC champs, but the artist formerly known as the Honey Badger was booted from the program last summer after his latest failed drug test. Mathieu said last month at the combine that he hasn’t smoked marijuana since Oct. 26, and he made it his mission to gain the trust of NFL teams. In a forthcoming interview, Mathieu was practical about the fact that his road to recovery would take time, that actions mean more than words and that his doubters won’t just disappear from a good sales pitch. And thus, Mathieu’s tour across the NFL map will include a stop in Foxboro. The 5-foot-9, 186-pounder played everywhere in LSU’s secondary, but he is most often viewed as a slot corner in sub packages at the pro level. That has become an increasingly important position with the explosion of spread offenses, and a guy with good ball skills like Mathieu could make an impact over the middle of the field. In two seasons at LSU, Mathieu had four interceptions, 11 forced fumbles, six fumble recoveries, two defensive touchdowns and six sacks, so he has proven he can show up all over the field. The Patriots just gave cornerback Kyle Arrington a four-year, $16 million contract, so they’re good in the slot. Yet, Bill Belichick has never been reluctant to load up at one position and let the situation play out. Since cornerbacks Aqib Talib and Alfonzo Dennard had injury issues last season, and Dennard has an April 11 sentencing on tap, it certainly wouldn’t hurt to add depth in the slot if Arrington has to bump outside.