Beckham, who missed 12 games last season mostly because of a fractured left ankle, is scheduled to make $8.5 million this year, which is well below market value for a player who is generally considered among the top receivers in the NFL.
"It's that time just to get it over with," Beckham told NJ Advance Media on Saturday night prior to the NFL Honors awards show. "I really want to do it so I can move past it. It's too much sitting around thinking, 'Where am I going to be at?' I need to know where I can start buying furniture for a house. I want to have a place set where I know, 'OK, this is home. I can always go back to home.'
"So it's just a little intermediate process right now. I'm sure it will get worked out."
A new regime is in charge of the process. The Giants recently hired general manager Dave Gettleman and coach Pat Shurmur. Both have reached out to Beckham in recent weeks to connect with the star receiver.
Beckham said his conversation with Gettleman was "great" and called him a straight shooter. When asked specifically about Beckham at his introductory news conference, Gettleman said he learned from former Giants general manager Ernie Accorsi that you don't give up on talent.
There is no denying Beckham's talent and passion. At times, that passion and fiery personality has gotten him in trouble, earning him unnecessary penalties, league fines and a one-game suspension in his four years in the NFL. Still, he's among the best playmakers in the NFL and would be a major part of Shurmur's offense.
Shurmur came away from their conversation thinking Beckham was "inspired to get ready to have a really good year." Beckham felt they were on common ground.
"I think we have an understanding of what we want to do," Beckham said on Saturday night in Minnesota. "Just to talk to him and being with a guy who just loves football, I watched what he did in Minnesota and it was exciting, so I'm definitely looking forward to that."
Beckham had 25 catches for 302 yards and three touchdowns last year. He had at least 90 catches, 1,200 yards and 10 touchdowns in each of his first three seasons, being named to the Pro Bowl each year.
Beckham broke his ankle in a Week 5 loss to the Los Angeles Chargers. He told NJ Advance Media he was doing well with his rehabilitation but didn't know whether contract negotiations had begun.
The Giants don't appear to be in a rush.
"We will deal with that at the appropriate time," co-owner John Mara said several weeks back. "That is not necessarily right now. I've said before many times that we want him to be a Giant. We will get something done at some point. I first want Pat to sit down with him and for them to have a good understanding of how we are going to act going forward. I have a lot of confidence that it will work out well, but we'll see."
Beckham expressed a desire to be the highest-paid player in football last year, while acknowledging that might not be realistic. Pittsburgh's Antonio Brown currently tops all wide receivers at $17 million per season.
When the Giants see Beckham on the field again is likely to be determined by his contract situation. He says his focus is on the start of the season, not the offseason workout program or the start of organized team activities.
"There's no point," Beckham said. "Really to be ready for the first game is really all I'm worried about, so I can be 100 percent."