Both Premier League clubs are said to be interested in the Chile international, who could be forced out of the door at Camp Nou as the Catalan giants pursue Liverpool striker Luis Suarez.
Widespread reports have claimed that Sanchez could be included in a deal that would take Suarez to the La Liga side, while Arsenal are believed to have made a £32m offer for the forward.
"Alex Sanchez would be a brilliant signing for Arsenal," Groves told talkSPORT. "He fits their remit. He's very good technically and has an excellent attitude.
"I think he'll go to Liverpool though. He'll be part of the deal that takes Luis Suarez to Barcelona."
Reports have claimed that Sanchez wants to stay at Barcelona, but would prefer a move to Arsenal should he be pushed out of the Spanish club.