Barcelona have one hand firmly on the La Liga title after winning 2-0 at Alaves on Tuesday, leaving them 12 points clear at the top of the table with four games to play.
Should second place Atletico Madrid lose at Valencia on Wednesday or against Real Valladolid on Saturday, Barcelona will be champions before they face Levante that evening.
However, Sergio Busquets said he would prefer to win the title at home to celebrate in front of the Camp Nou faithful than to win because of an Atleti slip.
He said: "We would like to win La Liga at home on our own merit and in front of our fans, but at the end of the day it's won when it's won. I hope that it comes as soon as possible but it's better to celebrate it at Camp Nou. What we've done in recent years [nearly eight titles in 11 years] is historic."
After a turgid first half, Barcelona stepped up a gear in the second and midfielder Carles Alena sent the Catalans ahead at Mendizorroza after 54 minutes.
Suarez added the second from the penalty spot after Tomas Pina's handball was spotted by VAR, putting Barcelona in touching distance of their 26th league title.
Samuel Umtiti bundled home from an offside position but after VAR ruled out the defender's goal, the handball by Pina was penalised.
Valverde brought on Messi, Alba and Arthur in the final stages to help Barcelona see the game out, with title celebrations poised for Saturday, or sooner. Alaves are eighth.
"We started well, we could have gone ahead in the first half," said Alena.
"It took a superb move [to break through], a great ball by Sergi that Luis left for me. He saw me coming behind him and he's such a world class player that he was aware of my movement.
"Let's wait and see what Atletico do tomorrow. If they fail, we're champions. I think we deserve this title, we've been the best team."