Costa, the £32million signing from Atletico Madrid, has scored four times in his first three games for Chelsea, but withdrew from the Spain squad during the international break with a hamstring problem.
"Diego came back injured, but that was last Saturday," Mourinho said.
"He had one week to work hard with the medical department
He has a chance to play tomorrow.
"We have a training session now (on Friday afternoon) to confirm his condition and to make the final decision."
Mourinho had little doubt Costa would adapt swiftly to the Premier League.
"When we bought him we were very optimistic," the Portuguese added.
"His profile as a player, his profile also as a person
A player (who) is also part of a team and we knew that the team was going in a certain direction and was waiting for a person like him to be there.
"His start was good
Three matches, three victories and four goals."
Loic Remy, who signed from QPR for a reported fee of £10.5million after Fernando Torres left for AC Milan on a two-year loan, is in contention to make his debut against the Swans, who have also won all three of their league games so far.
Costa could be kept in reserve for the opening Champions League fixture at home to Schalke next Wednesday, which comes ahead of the trip to Premier League holders Manchester City
Mourinho refuses to look beyond the visit to Stamford Bridge of Swansea, who he believes have strengthened this summer despite the loss of Michu.
"In this moment it's Swansea," Mourinho said.
"We have nine points we want to have 12
If it's not possible (to get) 12, (then) 10 at least
We go game after game.
"I don't think (Swansea) lost one of their most important players
They bought and they bought well.
"They invest seriously and they bought quality players."
Swans boss Garry Monk believes the fairytale at the Liberty Stadium is far from over as a movie about the club hits the West End on Friday night.
Jack to a King tells the story of a club which went from the brink of extinction to living the dream and has its London premiere in Leicester Square on the eve of Swansea's visit to tackle Mourinho's men
Monk has played a big part in Swansea's climb over the past 10 years as player, captain and now manager and still struggles to comprehend the club's rags to riches rise
"The Chelsea game fits in with the story because it's one you would not believe unless you witnessed it," Monk said.
"That's why I want people to watch it
It gives you a big insight.
"There's plenty of clubs who went up and through the leagues, we did it ourselves before.
"But the actual circumstances the club found itself in and what we had to go through will leave people surprised.
"This means a lot to a lot of people and it's probably the perfect time for a film."
Monk joined Swansea in 2004 a few years after the club nearly went into liquidation, salvation coming in the form of a combination between Supporters' Trust members and a consortium of local businessmen.
But he still had to endure some pretty basic training facilities before Swansea rose through the divisions and reached the promised land of the Premier League.
Swansea's story got some silverware in 2013 when the club won its first major trophy in 101 years of trying - the Capital One Cup when beating Bradford 5-0 at Wembley
That triumph took Swansea into the Europa League and Monk feels that achievement is possible again through a high Premier League placing, despite intense competition from clubs with greater financial resources than the Welsh club.
"If we stop now we have wasted all that hard work," Monk said.
"We are never going to be a financial power in this league, but we can make sure we are competitive.
"We experienced Europe last year and that was something we really enjoyed, and we would like to get back to at some point sooner rather than later.
"We have shown we can win a cup, but we would like to do it through the league as well.
"People say the Chelsea game is a top-of-the-table clash, but we are not going to be title contenders at the end of the season.
"We know exactly what we are, we are a club looking to progress and all the new players who have come in buy into that."
Source : PA
Source: PA