The 27-year-old memorably hit the ground running upon his arrival from Manchester City in the summer of 2022, but a combination of injuries, competition for places and underwhelming performances have all plagued his time in North London since.
Despite Bukayo Saka's absence and recent injuries to Kai Havertz and Gabriel Martinelli, Jesus was only brought off the bench for the last 10 minutes of Saturday's 2-0 Premier League loss to Bournemouth, when Mikel Arteta's men were chasing a lost cause.
That was the Brazilian's ninth appearance of the season without a goal or assist, although only three of those games have seen Jesus make the first XI, against Atalanta BC, Bolton Wanderers and Southampton.
However, with Liverpool on the horizon, Arteta will inevitably rotate some of his resources for the visit of Shakhtar, who have failed to win or indeed score in either of their two Champions League games of the season so far.
Jesus boasts terrific record against Shakhtar Donetsk
Jesus is one fringe player who will no doubt come into contention for a starting role against the Ukrainians, whom he boasts a brilliant record against from his time at Manchester City, having a direct hand in six goals against them from six previous games.
The 27-year-old has scored four of his own in addition to providing two assists against Shakhtar, firstly winning a penalty for Sergio Aguero to convert as a late consolation in a 2-1 loss in 2016-17.
The following season, Jesus notched a brilliant hat-trick in a 6-0 home crushing of Shakhtar in the group phase, two penalties and one injury-time effort, although one of those spot kicks was wrongly awarded for Raheem Sterling - now Jesus's Arsenal teammate - kicking the ground.
Man City and Shakhtar also collided in the group stage of the 2018-19 season, where Jesus scored City's third goal in a 3-0 away win before setting up an Ilkay Gundogan strike in a 1-1 home draw.
Should Jesus finally open his account for the season on Tuesday, he will become the joint-top scorer against Shakhtar in the Champions League, drawing level with Cristiano Ronaldo's current tally of five strikes.
Why Jesus should be hopeful of Arsenal start against Shakhtar
A brace or more would therefore see the Brazilian overtake the five-time Ballon d'Or winner, and he has every right to feel optimistic about making the starting lineup on Tuesday night.
Arteta has already confirmed that captain Martin Odegaard will not be back from his ankle injury in time for the visit of Shakhtar, and a midfield shake-up could see Havertz drop into a deeper role.
Thomas Partey could very well be rested with Liverpool in mind, leading to Declan Rice starting as the number six and Havertz dropping deeper to link arms with the Englishman and Mikel Merino, thereby opening up a spot up front for Jesus to fill.
Leandro Trossard and Martinelli are alternatives, but both endured nightmare evenings against Bournemouth; the former's horrible backpass triggered William Saliba's red card-worthy foul, while Martinelli missed a glorious chance to put Arsenal 1-0 up.
Jesus's fellow Brazilian may not be considered for two starts in quick succession after his recent calf injury either, so the stars are aligning for the 27-year-old to come into the first XI on Tuesday evening, but another disappointing performance and his Arsenal career could be in serious jeopardy.