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.
The Mail reported that Arsenal were willing to pay Manchester United a £6m loan fee to acquire Welbeck until the end of the season but then changed that report to £3m loan deal with a view to a £18m permanent deal.
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.
Welbeck's agent Jonathan Hope told talkSPORT that if his client moved, they would be looking for a permanent deal.
"There have been a few clubs in for Danny and they’re looking for loan deals with a view to buying, but Danny doesn’t want to go on loan.
"He wants a straight transfer and he has every right to say that."
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.
One of the many merits of Louis van Gaal is his ability to spot and nurture a youth prospect. While Danny Welbeck is an experienced international of 26 caps, it is fair to say that at 23-years-old there is huge scope for Welbeck to improve and be improved by Van Gaal. So despite the arrival of Radamel Falcao it is somewhat of a shock that the Dutchman has sanctioned this move, particularly as Welbeck broadly suits the requirements of a Van Gaal forward – Welbeck is mobile and tactically aware if a little wasteful in front of goal. From an Arsenal point of view, Welbeck is almost perfect for them. He is an improvement on the much-maligned Yaya Sanogo and also a proven Premier League performer while the move is not financially prohibitive particularly compared to the Falcao deal. However, is he the calibre of player that could push Arsenal from title contenders to winners? Probably not but his signing remains an astute piece of business.
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