Coutinho, 25, has made no secret of his desire to leave Anfield for the Camp Nou this summer and handed in a transfer request last week in order to try and push through a move to Catalonia before the end of the window, which closes in a fortnight's time.
Liverpool have rejected two offers from Barcelona for Coutinho already this summer and may hold on to their coveted playmaker even if they receive a bid worth £100m (€109.7m, $128.9m) from the Blaugrana during the dying embers of the transfer window.
With Jurgen Klopp's side refusing to budge, Merson, who enjoyed a number of successful years at Arsenal, thinks Ernesto Valverde's men should call off their pursuit of Coutinho and focus on trying to lure Chile international Sanchez back to Spain.
Sanchez has just one year left on his contract and Arsene Wenger recently admitted that Arsenal have made "no progress" in their attempts to tie the former Udinese wonderkid down to a new long-term deal.
The Frenchman insists he is prepared to make a "financial sacrifice" in order to keep Sanchez for the remaining year of his contract and risk him walking away on a free transfer next summer, but Merson thinks Barcelona should chance their arm and submit a £70m offer for Sanchez, a player he believes is superior to Liverpool's Coutinho.
"Do you ring up Arsenal with an offer of £70million for Sanchez?" Merson said on Sky Sports, relayed by The Express. "I know they're saying £50m won't buy him and we'll let his contract go out but £70m is a lot of money and I think that might twist it.
"Sanchez scores many more goals than Coutinho does and you're still getting £30m change. I'm looking at Sanchez, and I know he's been to Barcelona but surely you go and get him?
"He can play there and come in from out wide. He's still top drawer and a world class footballer."
Like Liverpool, Arsenal would be loath to lose their star attacker so late in the summer transfer window and may well bat away such an enticing offer for Sanchez, who is believed to have designs on a move to Manchester City.
Wenger has been staunch over his refusal to sell Sanchez, and the Arsenal boss is also keen to see Alex Oxlade-Chamberlain remain at The Emirates Stadium this summer. Like Sanchez, Oxlade-Chamberlain has just one year left to run on his contract with the Gunners and is believed to be attracting interest from Manchester United, who have grown frustrated in their pursuit of Inter Milan attacker Ivan Perisic.