Mulligan, 6-foot-4 and 270 pounds, is regarded as a quality blocker.
He was recently released by the Packers after spending training camp with the team. Originally signed as an undrafted free agent out of Maine by the Dolphins in 2008, Mulligan has also played for the Titans, Jets and Rams.
The Patriots have an open active roster spot, and with Rob Gronkowski not expected to play in Week 1, the team is light on established run blockers at tight end. That may explain why the team wanted to bring Mulligan in for a closer look.
As for Dill, he is an undrafted 2013 free agent out of Rutgers who was recently waived by the Jacksonville Jaguars.
He transferred to Rutgers after starting his college career at Maryland. He was a starter in all 12 games during his lone season at Rutgers, playing right tackle.
The Patriots are now at seven players on their practice squad, one short of the limit.