The Evening Standard, Sky Sports News and the Daily Mail are among those reporting the news about the England international , who has also been heavily linked with Tottenham Hotspur.
Welbeck will give Arsenal a desperately needed option up front with Oliver Giroud ruled out injured until at least the New Year.
Manchester United are willing to allow Welbeck leave the club due to the impending arrival of Radamel Falcao on loan from Monaco.
Press Association Sport understands the Gunners were also approached about the possibility of bringing in Toronto FC's Jermain Defoe on loan but did not express an interest.
The Gunners drew 1-1 at Leicester on Sunday to at least maintain their unbeaten start to the new campaign, which also saw them overcome Besiktas and secure a place in the group stages of the Champions League.
Manager Arsene Wenger flew to Rome on Monday to take part in the 'Match for Peace', which aims to promote religious harmony, with chief executive Ivan Gazidis and negotiator Dick Law on hand in London for any late moves.
There were no shortage of players being linked with the club.
Widely reported in-bound targets included: Borussia Dortmund defender Sokratis Papastathopoulos, Swansea frontman Wilfried Bony and West Ham's Winston Reid, Matija Nastasic at Manchester City and Aston Villa's Ron Vlaar, Paris St Germain's Adrien Rabiot and also defensive midfielder William Carvalho of Sporting Lisbon but none of the deals currently look like materialising.
However, Welbeck looks to be the most realistic option at this moment, although there is also an outside chance a deal could struck Nastasic who is also attracting the interest of Tottenham, Stoke and Newcastle.
It is expected 21-year-old Spanish defender Ignasi Miquel will complete a £1.5million switch to Norwich.
Arsenal have most of the first-team squad away over the next two weeks on international duty.
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