Gunners boss Arsene Wenger is lining Bacca up for a £20 million move in the January transfer window, Phil Cadden wrote for the Sun.
Per the report, Wenger is a fan of the 30-year-old Colombia international and attempted to sign him last year prior to his switch from Sevilla to Milan.
Bacca has averaged a goal every two matches in Serie A but has fallen out of favour with Milan boss Vincenzo Montella for returning to Seville and training with his old team-mates in November, Cadden noted.
His visit was documented on the Spanish club's social media.
The Gunners have used Alexis Sanchez through the middle this season and have the option of Olivier Giroud's aerial ability off the substitutes' bench. But the France international and his fellow backups have struggled for form, and often fitness, as he, Danny Welbeck and Lucas Perez have all been unavailable at times, per Transfermarkt.co.uk.
Sumeet Paul for ESPN FC noted that any Bacca sale could come down to what happens with Milan's takeover deal with Sino-Europe Sports, for which a shareholders meeting is scheduled on December 13.
Paul wrote: "In the event that that there is another delay or a new deposit isn't made before the sale is completed in January, there is the possibility that Bacca, one of the more high-value assets in this Milan squad, could be sold in the New Year in order to fund Milan's transfer business."
While signing Bacca would make a statement that Wenger is willing to strengthen after the club's good start, it is unlikely the French manager would revert to playing Sanchez in the wide positions having watched him become so effective at the centre of the Arsenal attack.
Bacca is a striker who comes alive in the penalty area, but his lack of work rate can be questioned. When put up against Sanchez's desire to help the cause, that means there should be no contest as to who would make the starting lineup if Wenger did secure Bacca's signature next month.
Sanchez has been in superb form this season, his hat-trick against West Ham United on Saturday took his tally to 11 goals and level with Chelsea's Diego Costa at the top of the Premier League scoring charts.
Bacca himself prefers to play centrally, so unless Wenger altered his tactics or Sanchez picked up an injury, the Milan man would probably have to settle for making an impact off the bench.
It may also be that, at the age of 30, Bacca would not be keen to play second fiddle to the younger Sanchez, who is 27. A £20 million fee would not represent a massive financial gamble for Wenger to add him to the squad, despite the manager's well-known prudent nature.
But at that price, Wenger is likely to face competition from fellow Premier League clubs who would be able to offer him more regular first-team action.
The Gunners boss could also look to renew his interest in Germany midfielder Julian Draxler after the wantaway Wolfsburg star was booed off the pitch by his own fans on Saturday, per Matt Maltby of MailOnline.
According to Maltby's report, Draxler said he was standing by his wish to leave the Bundesliga outfit. The 23-year-old added: "I don't think I need to tell anybody what [being booed] does to a person—it certainly doesn't help you."
Draxler has long been a target of Wenger's, and it now appears he could have an outside chance of landing the player to boost his squad next month. However, Wolfsburg are likely to play hardball and will be reluctant to let him go midseason.
However, while a move for Draxler may be more unlikely in January, Wenger looks to have Bacca fixed in his sights.