Catalan publication Sport says that the Serie A side were ready to pay around €30m (£27.5m, $35.7m) to lure the Under21 Spanish international to the Italian football but the player decided to turn down the offer after Messi advised him to remain at the Nou Camp.
Barcelona recruited Suarez from the Manchester City academy in 2013 as a prospect for the future but he was sold to Villarreal only two years later due to the huge competition for place in the first-team.
Last summer the La Liga giants decided to lure him back to the Nou Camp by activating a buy-back option after the midfielder impressed during his spell at the Yellow Submarine.
However, his future at Barcelona came under question again this summer amid the club's attempts to bolster the midfield further with the likes of Liverpool star Philippe Coutinho and Paris Saint-Germain ace Marco Verratti.
The Spanish publication claimed last week that Suarez decided to turn down Spurs and the Italian side as he was not ready to give up on his Barcelona dream just yet.
Sport has now provided more details about Suarez's decision after revealing that a conversation with Messi also played a crucial role in the Spaniard choice.
The Catalan publication says that the offer from Napoli came around the middle of the summer and was very tempting for both Barcelona and the player. The La Liga giants didn't want to cash in on Suarez but let the player to make the final decision with Napoli being ready to pay around €30m to complete the transfer.
Sport says that Suarez did consider the offer but finally decided to stay at Barcelona despite knowing that he won't be a regular starter for Ernesto Valverde.
The player asked some of his Barcelona teammates for advice and Messi's recommendation for him to stay at the Nou Camp is said to be crucial in the final decision.
Meanwhile, Sport says that Valverde also told Suarez that he features in his plans ahead of other players like Andre Gomes or Arda Turan. Suarez said in June that he wanted to stay at Barcelona after being told by the club that he was going to have a place in Valverde's plans.
"No [I won't leave]. Next year I will be at Barcelona because the club have told me so. I have been told that next season is very important for me and with the change of the manager anything can happen," Suarez said.
"It is true that there are rumours [about other clubs interested in my services], but no-one has contacted me. I will be at Barcelona next year. The club have communicated that to me and I want to continue because my goal is to succeed here.
"I've asked some [Spain Under-21] teammates like Inaki Williams and Kepa [Arrizabalaga] about Valverde and they speak highly of him. [Roberto] Soldado, who played under him at Valencia, also told me really good things about him. I hope we do well with him."