Both sagas have run for the duration of the summer transfer window, which closes for Premier League clubs on August 9.
"I don't know about Thibaut," Giroud said after Chelsea's 5-4 penalty shootout victory over Lyon on Tuesday. "It's true that we have not seen him at training. If he leaves it's going to be sad for us because he is a great keeper."
Meanwhile, Giroud is pleased that Hazard, who wore the captain's armband on his return from World Cup duty, is set to stay at the club, despite having played a role in eliminating his Belgium side from Russia 2018.
"We want to keep him at Chelsea. It's a great feeling to play with this kind of player," he said.
"Eden and I texted each other after the World Cup. He congratulated me and N'Golo Kante. I didn't want to tease him about the semi-final. He had a very good World Cup and obviously he is a very special player."
Chelsea's new manager Maurizio Sarri predicted after the Lyon fixture that he expects a flurry of activity from his club, who are also in talks to secure Mateo Kovacic from Real Madrid on loan.
The 31-year-old only joined Chelsea six months ago, but his 18-month contract means that he has less than one year left on his current deal.
The World Cup-winning striker says he is calm about renewing and added that he has an option to extend his stay written into the agreement.
"I still have one year to go with Chelsea plus maybe another one," Giroud added. "I'm going to discuss that with the club at the right time.
"There is no rush. I just need to prepare well and be ready as soon as possible for the team. That's the most important thing right now.
"I am happy here at Chelsea. I just arrived a few months ago and am just starting to settle well. I think we had a good end to the season even if we didn't finish in the top four. We are hoping to have a great season for the fans and I'm looking forward to the first game."
Giroud's return to Chelsea comes after the euphoria of winning the World Cup with France, but it also may set him behind in his bid to start games, having only returned to training on Monday.
His Chelsea team-mates planned a special celebration for him and Kante, who were pivotal in France's World Cup win, on their return.
"It was a very short break but I was aware before the World Cup that I was only going to have three weeks off," he continued.
"I tried to enjoy it as much as I could with my family and my friends. Obviously, I only came back on Monday. I didn't expect to play last night but I feel good. We need to work physically to be ready as soon as possible, but it's nice to be back.
"I'm someone who doesn't like to show off. I'm quite humble, N'Golo is even more humble than me. Everyone just said congrats and they gave me a fake World Cup and they put it above my locker. We are very proud of it, me and N'Golo. It's for life you know!
"But the most important thing is to open a new page with our club and to be ready to give everything for the club."