The 23-year-old has risen through the youth ranks to become Sergio Conceicao's undisputed number one, and he has established a reputation as one of Europe's brightest up-and-coming goalkeepers.
Costa has kept 47 clean sheets in 109 competitive matches for Porto across all tournaments, including 20 shut-outs from 41 matches during the 2022-23 season.
The Portugal international has already won six pieces of silverware with Porto during the embryonic stages of his career, including two Primeira Liga titles, but Conceicao's side finished second to Benfica in the most recent campaign.
Costa also appears to have ousted Rui Patricio as Portugal's first-choice goalkeeper, starting all five of their 2022 World Cup games as A Selecao reached the quarter-finals.
Back in November, Porto tied Costa down to a new long-term contract until the summer of 2027, and those terms apparently include a €75m (£64.8m) release clause.
A recent report claimed that Man United were preparing to trigger that option, but Costa has now played down talk of a summer exit and is hoping to continue at the Estadio do Dragao.
When asked by reporters about Man United's interest following Sunday's Taca de Portugal final win over Braga, Costa responded: "That's the internet.
"It is a happiness and an honour to play for my favourite club. What they say is what they say, there is nothing concrete, I have a contract until 2027 and I hope to continue, let's see."
While a new striker is expected to be Man United's priority in the transfer market, the Red Devils are being tipped to sign competition for David de Gea, whose recent performances often made headlines for the wrong reasons.
The Spaniard won the Premier League's Golden Glove with 17 clean sheets, but he was widely criticised for a succession of mistakes, having made four errors leading to a goal in all competitions.
As things stand, De Gea will be free to leave Man United when his £375,000-a-week contract expires at the end of the month, but he is expected to put pen to paper on an extension, albeit on reduced terms.
Ten Hag insisted that De Gea had a "fantastic season" for Man United, having also won the EFL Cup, but the Dutchman has refused to guarantee the 32-year-old the number one jersey for next season.
Man United also have Dean Henderson and Tom Heaton in their goalkeeping ranks, but the former - who spent the 2021-22 season on loan at Nottingham Forest - is expected to head for the exit door after failing to displace De Gea on a regular basis.
Brentford's David Raya, Everton's Jordan Pickford and Inter Milan's Andre Onana are also believed to be on Man United's goalkeeping shortlist, although the Red Devils will have to rival Chelsea for the signature of the latter.