The Brazilian has been linked with a move away from Anfield as the latest reports suggest that Liverpool have rejected a second bid worth €100m (£89.3m, $118.25m) for Coutinho from Barcelona as they seek a replacement for Paris-Saint Germain bound Neymar.
Meanwhile, the Gunners have been trying to fend off interest for Sanchez who reportedly wants to reunite with former Barcelona manager Pep Guardiola at Manchester City.
The difference between the two players, however, is that Sanchez is entering the final year of his contract while Coutinho signed a new deal recently that will keep him at Liverpool until 2022.
"Liverpool did an amazing bit of business by signing Coutinho to a new contract, especially when you look at Sanchez and Arsenal and the problems it's causing around the club," Owen said, as quoted on The Mirror.
"Since Coutinho signed the new contract Liverpool have qualified for the Champions League, bought more quality players and are in a better place than they've been for a long time. With Arsenal I'm just not sure about the overall feeling within the club.
"My gut feeling is they could win five straight games, but if they lose the sixth the Wenger out brigade will come out which creates a negative atmosphere and that's probably the main thing going against Arsenal."
Owen did, however, praise the north London club's signing of Alexandre Lacazette, claiming that he could be a very good signing.
"I like Lacazette, he's a predator who knows where the ball is going to drop in the box," he added. "I think Olivier Giroud gets some harsh criticism but they needed another top class striker, and Lacazette is a very good buy."