I think Arsenal want to sign Coutinho as a back up for ôdegaard, I am sure Arteta wouldn't toy with the winning team, in case of any injury to any key midfield player, he will be a perfect replacement else Coutinho coming to sign Arsenal wouldn't guarantee him a regular shirt and I am sure he will weigh his option before signing the contract once he is not sure of first team shirt I think he will back out from the contract, as it is now Smith Rowe and ôdegaard are in-form now and very consistent I don't think any incoming player can displace them from the team.
They still have Smith Rowe and right now Arteta already is having difficulty giving them regular play time so why add another player to that list and make that worse? Also Coutinho is a big name (well not that big name) but still some player so I really don't think midfielder is what they need.
Yeah they do need a striker and Vlahovic really could be a great signing.
Because they could be played in a bit of a different positions. You could use Coutinho at the left wing, whereas you could play Smith Rowe behind the striker. Smith Rowe is a great player if you ask me, you could play him anywhere you want, but this is more like "we need a new winger back up" situation.
Plus, teams are having hard time with the covid protocol right now, with more and more players getting it, I am assuming that the team with the deepest bench would be at big advantage. Sure it would require to spend millions to be there, but some teams just have that kind of money I suppose. Doesn't mean that they will do it, it is just a gossip and as with everything in football, gossip usually doesn't turn out to be true.
However, if they actually manage to get him for cheap, then they could put him on the roster, and just use him if something bad happens.