The London club have seen two bids for Manchester United forward Wayne Rooney rejected, despite the 27-year-old having handed in a transfer request at the end of the 2012-13 campaign.
But those disappointments have not discouraged Mourinho, who reiterated his desire to add another forward to his squad following his side's 2-0 win over Hull City on Sunday in their opening game of the new Premier League season.
First-half goals from Oscar and Frank Lampard gave Mourinho a comfortable start to his second spell in charge of Chelsea.
When asked whether Chelsea are still pursuing Rooney, Mourinho replied: "We will try until the last day to add a new player to the squad, a striker.
"But in this moment every striker has a club, every striker belongs to somebody and I don't think it's ethical that I name players that belong to other clubs.
"If we have to make the bid we make it in an official way. We don't speak to players, we speak to clubs.
"We don't try like many clubs do go around and try to influence players to behave in a certain way we go direct to the club in the correct manner and we are going to try that until the last day of the transfer window."
The Portuguese went on to thank the Chelsea fans who gave him a rousing reception at Stamford Bridge prior to his first competitive fixture in charge of the club since September 2007.
"It's fantastic. It gives me more responsibility but at the same time they know I give everything for this club," he added.
"The reception was amazing. I was expecting that because I played here with Inter as an opponent and it was fantastic so I could imagine that coming to Chelsea would be like that.
"When the game started I focused on the game and from now on I think they have to support the team, support the players, bring the players' songs back and support them because I know they like me a lot and they know that I give everything for the club.
"So let's support the team and we need that every game, especially Wednesday because we have a difficult opponent."
Mourinho will oversee his second competitive fixture of the season when Chelsea host Aston Villa at Stamford Bridge on Wednesday in the Premier League.
