Manchester United boss Louis van Gaal has reiterated his desire to keep David de Gea at Old Trafford.
QPR are interested in signing West Ham midfielder Mark Noble, Sky sources understand.
The Northern Irishman said American owners Fenway Sports Group had the chance to appoint the Spaniard in the summer but opted to recruit him from Swansea instead.
Benitez, whose appointment as Chelsea interim manager earlier this season prompted an unprecedented hostile backlash from Blues fans, has suggested he could take charge of his former club again.
"My idea is to keep coaching a competitive team. Why not in England?" Benitez, whose success in winning the Champions League in 2005 means he still holds a special place in most Liverpool fans' hearts, told Spanish newspaper Marca.
"I will return to Liverpool one day almost certainly, I just don't know when, my daughters and wife are still living there."
Rodgers was appointed in the summer when FSG decided to dispense with Reds icon Kenny Dalglish and look for a different way forward.
Their faith in the appointment, even after a frustratingly up and down season, has given him the necessary confidence to not be intimidated by former managers looming large in the background.
Benitez is set to leave Stamford Bridge at the end of the season but the current Reds boss does not feel threatened.
"I haven't seen the statements but I've heard plenty of people talk about it," Rodgers said.
"Rafa had a successful time here in the period he was here and I think he will join a list of probably many managers throughout the world who would love to manage a great club - especially having been here before.
"Obviously that opportunity was there in the summer if the owners wanted to go down that route as Rafa was unemployed and not working.
"But they felt it best to go in a different direction and develop the club in a different way.
"And from that the board, players, myself and the club have all become one in looking to move forward and build success for the future.
"It is understandable any manager wanting to manage the club because it is truly a world-class football club.
"It is not a hindrance to me. Before I came here I had seen comments about Rafa wanting to be manager and I've seen comments while I've been here.
"But it doesn't affect me in my work or my job. My relationship is very strong with the players, we work very closely together on improving our football.
"We are very stable in terms of our board and the manager connection and we have some of the best fans in the world.
"It is a pleasure for me to be here at a truly remarkable club that many managers would want to manage, not just Rafael Benitez."
Rodgers has also dismissed a report winger Raheem Sterling has already been ruled out of this summer's European Under-21 Championships because of a thigh injury which has been troubling him in recent weeks.
"Not at this point, no," was his response when asked whether a decision had been taken on his international involvement.
"The medics wanted to take him out for a few weeks just to see where he was at with injuries. It has been an ongoing one.
"He's a very young player so we don't want to risk any long-term injury when there's no need.
"Of course you would rather have him in the squad to develop him, but this is a part of making sure we have a duty of care for him as a young player.
"When he shows signs of fatigue and a little bit of injury, we have to look at that and treat it in the best way we think possible.
"At the moment, that's to take him out."
Next month's Merseyside derby at Anfield, which could well decide which club finishes highest as Everton currently have a three-point advantage over their near-neighbours, has been moved back to Sunday May 5, kicking-off at 1.30pm for live television.