The Giants' pass rush depth has been a quiet concern this offseason, and they may be in the market to address it further.

They may also be interested in adding a veteran linebacker to the mix.

Former Lions defensive end Devin Taylor will make a free agent visit to the Giants on Monday, according to ESPN's Adam Schefter. The Giants are also scheduled to host linebacker and Paulsboro, N.J., native Gerald Hodges on Tuesday, according to Pro Football Talk. Hodges has been on a visit tour of late, and is said to be in Buffalo with the Bills on Monday.

Monday is the Giants' first day of organized team activities. The team currently has $9.483 million in available cap space, according to NFLPA records. That number will go down somewhat once the Giants sign first-round pick Evan Engram to his rookie deal.

Taylor, 27, started 16 games last year for Detroit, but was not re-signed. Taylor had 4.5 sacks in 2016, and has 15 in his career. Taylor posted seven sacks as a reserve rusher in 2015. The 6-foot-7, 266-pound end was a fourth-round pick out of South Carolina in 2013.

The Giants' pass rush was much-improved in 2016, but there remains ample room for improvement. The Giants had 35 sacks as a team in 2016 (tied for 14th in the NFL). Starting ends Jason Pierre-Paul and Olivier Vernon had 15.5 sacks together. The Giant defensive backs had eight. Reserve ends Owa Odighizuwa, Romeo Okwara and Kerry Wynn combined for 1.5.

The Giants believe fifth-round pick Avery Moss can be a valuable addition to their pass rush, but they can only expect so much from a rookie. Taylor found the most success with the Lions as a situational player, not a starter. That is the exact role the Giants would likely peg him in, were they to sign him.

Adding Taylor to the roster would also heighten the competition at defensive end and push players like Odighizuwa, Okwara and Wynn squarely onto the roster bubble entering training camp. Pierre-Paul and Vernon will be on the roster, as will Moss barring something unforeseen. That would leave Odighizuwa, Okwara, Taylor and Wynn likely fighting for two spots.

TALK IS CHEAP: Our first live look at the Giants' draft picks

Subscribe to the podcast on iTunes, Google Play, Soundcloud or iHeartRadio.

James Kratch may be reached at jkratch@njadvancemedia.com. Follow him on Twitter @JamesKratch. Find our Giants coverage on Facebook.