The former Liverpool manager has not enjoyed a comfortable start to his time with the West London side after being jeered by some sections of the Chelsea support in his first home game in charge, a goal-less draw with Manchester City on Nov. 25.
Ahead of their FA Cup fourth-round replay against Brentford tomorrow, Chelsea are on a run of two successive wins, but the previous sequence of just one victory from six matches, including a 2-2 draw against the League One side, have left Benitez in a vulnerable position.
Benitez has hinted to becoming the permanent manager at Chelsea when his short-term deal runs out at the end of the season, as reported by itv.com.
But the emergence of a link with Pellegrini has left a doubt whether Abramovich and the Chelsea hierarchy see the Spaniard as a future fulltime manager.
Pellegrini has guided Malaga into the last 16 of the Champions League and the top four of La Liga this season, but a question mark over the club's participation in UEFA competition due to the financial fair play ruling, as BBC Sport reported in December, has left the Chilean coach's future in doubt.
After a successful coaching career in South America, Pellegrini made an immediate mark on European football when he took Villarreal to the Champions League semifinals in 2006, less than two years after being appointed by the Spanish club.
Pellegrini was named Real Madrid coach in June 2009, but losing out to Barcelona in La Liga title race despite collecting a club record 96 points and Champions League elimination to Lyon at the last-16 stage helped to cost him his job when Jose Mourinho became available, as The Guardian reported in May 2010.
But the enquiry about Pellegrini leaves Benitez in a no-man's land at Chelsea. The former Liverpool manager's arrival at the club was not accepted well by many supporters, who were still angered by comments he made about the London club while he was in charge at Anfield.
Benitez's opening three games produced only two points but a subsequent record of seven wins from eight games eased the pressure on him. However, Chelsea fans' ire has become stoked again after a recent run of four matches without victory.
Benitez has already been accused of lacking passion, as Bleacher Report columnist Rowanne Westhenry highlighted in her recent feature, so how does he lift himself for the remainder of a campaign with another name linked to the role?
Pep Guardiola had been the shadow hanging over Benitez following his arrival, but after the former Barcelona coach's decision to join Bayern Munich next season, the Spaniard is now facing another name in the frame.
The future looks bleak for Benitez at Stamford Bridge, but it rarely looked golden.