The Gunners are languishing in 15th in the Premier League, with just four victories and one draw from their 11 games.
In the last two months, the north Londoners have won just one match - a 1-0 victory over Manchester United on 1 November.
A particular problem has been a lack of chance creation, with many supporters pointing to the exiling of Mesut Ozil as a mistake that has led to the issue.
However, Deeney pointed to another area that Arteta needs to look at, defensive errors. This comes after years of jibes at Arsenal, including claiming that they don't have "cajones" on one occasion.
In his The Sun column, Deeney wrote: "They remain something of a soft touch - but a different sort of soft touch.
:grimacing: "Arsenal are in trouble, they are very much in trouble."- talkSPORT (@talkSPORT) December 7, 2020
"Arteta has to come under criticism because of where Arsenal are."
:flushed: "If Arsenal lose to Burnley then Arteta is massively under pressure."
Troy Deeney thinks #Arsenal could SACK Arteta if they lose next Sunday. pic.twitter.com/SXmxdFQMLf
"Not a team you can physically intimidate but a team who will always give you a chance."
He added that Arteta could be in danger of losing his job if he doesn't turn things around against Burnley this weekend.
"Burnley will believe they can win at the Emirates tomorrow. They will look to exploit Arsenal's weaknesses from set-pieces and they will look to hit them on the break, too.
"If Arsenal play to their full potential, they should win. If they lose, then Arsenal could slip towards a genuine relegation battle and Arteta will be in serious trouble."
Some fans have been becoming frustrated with Arteta in recent weeks, comparing him to his former boss David Moyes ahead of mentor Pep Guardiola.
Arteta has more of a similar style to Moyes than Pep. pic.twitter.com/89vpdG02Ct- Mas (@ForzaMas) December 6, 2020
everyone thought Arteta was Pep's apprentice when the real Sith is in fact Moyes pic.twitter.com/HASst3111I- big slug (@kierposting) December 6, 2020
Arteta defo learnt more from Moyes than Pep. pic.twitter.com/gZBGpgiLMt- David Wilkinson (@DavidWilkz) December 6, 2020
The Watford striker signed off: "Burnley is a massive game for Arteta. Win it and Arsenal could soon be back in the top half and he can continue to affect change at the club.
Lose it and the game might be up."
Could Arteta be on the way out if Arsenal lose to Burnley on Sunday?
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