The wide receiver is hoping for a new deal by the end of this season and told ESPN's Josina Anderson that negotiations are progressing.
"I was excited to hear this weekend that contract talks are moving in the right direction," Cruz told Anderson on Monday. "I heard there was some progress on the structure."
Cruz is still hopeful about receiving a longer-term deal, according to Anderson's report. He has maintained that he wants to remain a Giant for several more years.
The Giants' playmaking receiver is in the final season of a contract worth $540,000. He will be a restricted free agent after the season unless both sides work out a new deal.
Cruz has tried his best not to make his contract an issue and refuses to let it become a distraction.
"It's not on my mind," Cruz said last week. "I have no clue when it's going to get done. I'm just playing football right now. I just want to continue to play football and worry about that later."
Cruz is one of the most underpaid playmakers in the NFL, if not the most underpaid one. He broke out last season with 82 receptions for 1,536 yards and nine touchdowns and helped the Giants win the Super Bowl.
"I just kind of block it out," Cruz said. "I'm just out here enjoying the moment, enjoying times. I still feel like I'm out here as [an undrafted] free agent just still trying to work hard every time I'm on the practice field, every time on game day.
"I'm just continuing to be my same person, just continuing to keep my family close," he added. "And I think that's really helped me."