The striker role has proved somewhat problematic for the reigning European champions, with Chelsea's Diego Costa failing to replicate his domestic form on the international scene and question marks raised over his on-field conduct.
Veteran Athletic Bilbao striker Aritz Aduriz, who has 17 La Liga goals to his name this season, was handed a recall to the national team after a near five-and-a-half-year absence during the international break and he responded by scoring in a 1-1 draw against Italy last Friday.
Valencia forward Paco Alcacer is another candidate to start up front, but Morientes feels Juventus' Morata should be given the nod at the Euros in France despite scoring just once in eight appearances for his country.
"I think that in terms of characteristics right now, Morata is one of the clear candidates for the number nine position," Morientes told Omnisport.
"For the players he has around him as well. He's a penalty area player who plays well high up the pitch. He's a goalscorer and a complete player.
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"And apart from that he's a player you can use out wide. He's very quick and he can go past players. For me, he's the most important player in attack for the national team.
"But we can't forget Aduriz, a player who's having an exceptional season. Alcacer is another player with very special characteristics inside the box.
"And Diego Costa, apart from all the other good things he has, is very important as well with his ambition and his personality. It's very important to have that in a team too."
Ex-Real Madrid striker Morientes also had his say on the goalkeeping situation as Del Bosque weighs up whether to go with Iker Casillas, who has faced criticism from sections of the Spanish press, or Manchester United's David de Gea.
"Whoever plays of the two will give a lot of solidity to the national team," Morientes added.
"One [De Gea] has the youth and talent of someone who's being called one of the best goalkeepers in the world right now and the other [Casillas] has the experience of the huge challenges he's already faced with the national team.
"The two European Championships he won, the World Cup, having played with Real Madrid for so many years. That gives Iker an authority that not many goalkeepers have on the world stage."