Chelsea are close to completing the £32m signing of the Atletico Madrid frontman after he passed a medical and agreed personal terms on a switch to Stamford Bridge.
Despite being hampered by a persistent hamstring injury during the closing weeks of the 2013/14 campaign, Costa is expected to lead the line for world champions Spain at this summer's finals in Brazil.
Mourinho is hopeful that the 25-year-old will feel no affects of that troublesome hamstring problem during the World Cup.
But the Chelsea boss still remained tight-lipped over Costa's move to Chelsea.
"I hope [Costa] has a normal World Cup, no injuries, good holidays and I hope next season he can have a fantastic season," Mourinho said in his Yahoo blog.
"I don't know where, but I hope he can have a fantastic season next season."
Though Mourinho is remaining coy over the deal, the Brazilian-born forward, when asked if he will join Chelsea, revealed: "Well, it looks like it."
Costa is set to be joined at Chelsea by Atletico team-mates Filipe Luis and Tiago.
Former Chelsea midfielder Tiago, 33, will rejoin the Blues - the club he left in 2005 after just one season - on a free transfer.
While left-back Luis, 28, is close to completing a £20m switch after Atletico secured his replacement at the weekend in Granada defender Guilherme Siqueira.