Fernandes, 24, has scored 31 goals and made 17 assists in the Primeira Liga this season and is said to be keen to join City, having been made aware of the personal terms on offer at the Etihad Stadium.
Manchester United are also keen on the player but City are in the driving seat after recent talks between club officials and super agent Jorge Mendes, who is not Fernandes’ representative but has been called in to broker a move.
Sporting initially asked for €70 million (£60m/$78m) for Fernandes, but City are hopeful an offer of €50m (£43m/$56m), plus two players, either on loan or permanent deals, will be sufficient.
Mendes is involved in both potential transfers and has met with City officials, including sporting director Txiki Begiristain, on several occasions.
Sporting’s sporting director Hugo Viana has been present at at least one of the meetings regarding a move for Fernandes. City are keen to strengthen their midfield and the Portuguese club open to a sale.
Portuguese reports have claimed that Marlos Moreno, who has been loaned out by City since joining in 2016, Eliaquim Mangala, a Mendes client who joined from Porto in 2014, and Douglas Luiz and Aleix Garcia, who have been on loan at Girona, could be part of any deal.
City midfielder Bernardo Silva was with Fernandes at a tennis tournament in Portugal last week and hailed his fine season with Sporting during an interview with the press.
"Bruno is a great player," Bernardo said.
"He has had a fantastic season with many goals, many assists that are not normal for a player of his position, he has the best numbers and we’ll see what happens at the end of the season.
"He is a player who can play in other championships.”
Goal previously reported that several City first-teamers are keen for their employers to sign Felix from Benfica this summer, and Bernardo was very complimentary of the Eagles' young players.
"It is very good the bet that Benfica has made on youngsters, from Ferro, Joao Felix, Florentino, to Jota, who has played less," he added. "I wish I could take the youngsters from Benfica to Manchester. They are all very good."
City still plan to sign Rodri from Atletico Madrid as a long-term replacement for Fernandinho, and should they close a deal for Fernandes it could open the door for Ilkay Gundogan to leave the club this summer.
Club chiefs had been making efforts to renew Gundogan's contract, which expires in 2020, despite the midfielder making it clear earlier this year that he would not sign a new deal over concerns surrounding a lack of playing time.
City are expecting several current first-team players to leave this summer and are prepared to spend £100 million ($131m) net ahead of next season.
That means that their summer transfers, to an extent, rely on how much money they can recoup for their outgoing players.
Nicolas Otamendi and Fabian Delph are set to leave, while Danilo has been linked with Inter. Gundogan’s situation remains unclear, but Fernandes’ arrival could signal the end of his time at the Etihad Stadium.
Gabriel Jesus’ position could also be under threat, but only if City can identify the right forward, for the right price, and receive an acceptable offer for the Brazilian.
City had been planning to bring in a new left-back for many months, but pulled the plug on a move for Ben Chilwell in the past fortnight, partly so they can use the funds elsewhere.
As well as Rodri and Fernandes, the Blues want to sign a central defender and a forward.
Talks have been held regarding a move for Felix, although City do not want to pay his buy-out clause of €120m (£102m/$134m).
Felix is not the only name on City's forward shortlist, although the club have abandoned hope of signing Luka Jovic from Eintract Frankfurt, despite heavily scouting the Serbia international throughout this season.
Benfica’s deep-lying midfielder Florentino has also caught the eye of City scouts in recent weeks, and while no move is planned just yet, they are keen to put the foundations of a future transfer in place.
The English club are aware that Florentino could sign a new contract in the next 12 months that would raise his release clause from €60m to €100m.
To avoid having to pay that higher figure, the Blues are exploring ways to secure a first option that would allow them to strike a deal for something closer to his current valuation, should they decide to make their interest concrete in the future.