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But now it appears Roma are reluctant to let the 22-year-old leave the club.
The Serie A side are reportedly keen on taking Ramsey to the Stadio Olimpico, with the 27-year-old out of contract in the summer.
A swap deal was touted between the two clubs, but now Monchi has dismissed the reports.
The deal would have seen Schick join the Gunners on loan in January, with Ramsey going the other way on a free transfer.
However, speaking to Gianluca Di Marzio , Monchi said: “Schick? We have confidence in him, he won’t leave on loan.”
The news comes as a blow to Arsenal boss Unai Emery, who is hoping to add reinforcements in the transfer window after the injury to Welbeck.
Welbeck is unlikely to feature for the North London side again this season amid fears he suffered a broken ankle in the Europa League clash with Sporting.
Czech star Schick would have provided back-up for first-choice strikers Alexandre Lacazette and Pierre-Emerick Aubameyang.
Roma will now face competition for Ramsey – who is expected to stay at the Emirates until his deal expires in the summer.