According to Corriere dello Sport (h/t Football Italia), the Serie A outfit are considering an exit for Schick, who has endured a difficult time at Roma following his move from Sampdoria ahead of the 2017-18 campaign.
Sevilla and Real Valladolid are noted as possible suitors from La Liga, although Arsenal are also said to be in the frame. It's added that if the Gunners were interested, Roma would ask for Ramsey to head to the Stadio Olimpico as part of the deal.
Arsenal are poised to lose Ramsey either in January or at the end of the season. The Welshman's contract is set to expire in the summer, and it's been reported that the midfielder is preparing to depart the Emirates Stadium at the end of the campaign, per Lyall Thomas of Sky Sports.
The Gunners may be on the lookout for another forward in the January transfer window following the seemingly serious injury suffered by Danny Welbeck in the UEFA Europa League on Thursday.
According to Sami Mokbel of the Daily Mail, Arsenal are poised to be without the England international for the rest of the season.
Manager Unai Emery praised Welbeck following the injury:
If Schick was indeed available, then he would represent an interesting option for a number of clubs, including the Gunners.
When Roma landed him in the summer of 2017, he was deemed a major coup, having excelled for Sampdoria previously. However, he has suffered injuries and a subsequent loss of form, meaning it's been tough for the 22-year-old to force his way into Eusebio Di Francesco's XI.
So far this season, the Czech Republic international has started just two games in Serie A; per Italian football journalist Adam Digby, the team appear better without him in the side:
Arsenal do have Pierre-Emerick Aubameyang and Alexandre Lacazette on their books, giving Emery plenty of firepower up top. However, you suspect the Spaniard would be keen to add another versatile option to step in for those players or come off the bench.
Given Ramsey has been on the bench for Arsenal's last four Premier League games, losing him in January may not be a massive blow to the team's cause. If they could acquire a prospect like Schick in exchange for him midseason, it may make sense for both parties.
At the moment, all reports point to a summer departure for the Welshman, and if Arsenal are to enjoy a successful campaign, then his ability to surge forward from midfield positions and score goals will be crucial.