And on Saturday he opened the scoring at Stamford Bridge in a Premier League clash between the two.
Twitter was awash with reaction to Sturridge's brilliant goal.
Despite dominating for lengthy periods and creating a series of chances to equalise, Liverpool struggled to make the breakthrough due to the home side's defensive discipline. Chelsea equalised soon after through Emerson although VAR played its controversial role in holding up the goal.
"But then I talk with the board here, with the manager, and I say OK you don't want me to leave, I can stay no problem".
Jurgen Klopp's side have made a flawless start to the season in the league after six games and Giggs, a 13-time title victor with United, views their ability to win in different ways as an asset.
Pedro, now injured, is perhaps Sarri's best hope, but again, he can not be relied upon to score 15-20 goals.
Both teams made sweeping changes on Wednesday, but not too numerous players that ran out midweek are likely to feature at the weekend as the the intensity gets cranked right up.
Klopp also attempted to downplay Mohamed Salah's withdrawal after 66 minutes, with Xherdan Shaqiri replacing the Egypt worldwide, who squandered a number of good opportunities during his return to Chelsea.
"It was a hard game for both sides".
There was some talk on social media post-match of being anxious ahead of the visit to Stamford Bridge this weekend but I'm not really sure why.
The Brazilian-born Italian global has completed well over 200 more passes than any other midfielder in the Premier League this season including a league record of 180 against West Ham.
Perhaps the most anticipated among the individual contests remain the battle between Alisson and Kepa Arrizabalaga - none of whom were a part of the starting lineup on Wednesday.
Speaking on BT Sport, Hazard said: 'When you win 1-0 until pretty much the end but then concede you can be sad but also I think they should have scored before. David Luiz's substitution in the League Cup added another dimension to Chelsea's play and the energetic Brazilian has morphed into a key player in Sarri's Chelsea.
Dejan Lovren featured in a competitive fixture for the first time since July and as expected of a man coming back from injury, looked horrendously off the pace while Alberto Moreno provided a timely reminder of why Andrew Robertson is a must have in Klopp's regular backline. @xKyzo10 chipped in with 'Hazard in game management is second to none, he's the best closer in football history'.
The draw ended Liverpool's 100% start to the Premier League season - and they finished the day behind defending champions Manchester City on goal difference.
Salah was always likely to have his form scrutinised more closely this season given his stunning exploits in 2017-18, and this performance will have done little to keep the critics off his back.