Following their involvement in the FIFA World Cup the pair will return to the Gunners facing uncertain futures under new manager Unai Emery, according to Jeremy Wilson of the Daily Telegraph.
"The club are focused on trimming the squad after completing their main incoming transfer business," Wilson wrote. "Emery has spent around £70 million on five senior signings, who are aimed at adding defensive resilience to the team he inherited from Arsene Wenger."
After Arsenal's signing of Bernd Leno from Bayer Leverkusen the Gunners are likely to sell a goalkeeper, and at this point Ospina appears to be a more likely departure than Petr Cech. According to Calciomercato (h/t Tashan Deniran-Alleyne of Football London), Napoli are keen on the Colombia star.
Meanwhile, Welbeck is entering the final year of his contract at the Emirates Stadium having joined from Manchester United in 2014 and is a long way down the pecking order in the forward positions. Emery has Alexandre Lacazette and Pierre-Emerick Aubameyang available to lead the line.
After a blistering beginning to his time at Arsenal following his January move, it doesn't appear as if Aubameyang's prolific goalscoring will be slowing down any time soon either:
It's a crucial summer for the Gunners, as they get set for a campaign without Wenger at the helm for the first time in 22 years. Emery has already been putting his mark on the squad too, with Stephan Lichtsteiner, Lucas Torreira and Sokratis Papastathopoulos already arriving.
Now the club clearly have some big decisions to make regarding potential outgoings, with Ospina and Welbeck likely to be on the fringes if they do stick around.
The former may find himself as third choice following the signing of Leno. While he does have his flaws as a goalkeeper, Ospina is a proven Colombia international and has been dependable in the Premier League.
Welbeck is another who is a solid albeit not spectacular option. The England international is combative, hard-working and versatile, making him a useful player for managers to have around. However, throughout his career at Arsenal he's lacked a vital cutting edge in front of goal and has been hampered by injuries.
The Sportsman Twitter account put Welbeck's goalscoring record into some context:
During the World Cup, Arsenal writer James McNicholas joked about the respective calibre of the two players linked with an exit:
Emery does appear keen to quickly mould this Arsenal squad in his image, and it'll be intriguing to see how ruthless he is in letting squad players like the duo mentioned move on.
Even so, both players are capable of doing fine jobs elsewhere in the Premier League or potentially even abroad. At this point in their respective careers, leaving Arsenal and getting regular football elsewhere is surely the smart choice.