This season's Spanish champions and Champions League finalists, who also look set to lose David Villa to New York City FC, are keen to build on their recent success. Cross believes Negredo is a player high on their list of priorities.
Negredo had a strange first season at City. Up until January, he was playing superbly well, netting 23 goals in his first 36 games, before a 16-game drought left some doubts over his ability. It's rare to see a player's form collapse so suddenly, and he looked bereft of confidence in the closing weeks of the campaign.
It's clear, though, Negredo has qualities well-suited to the English game: His pace and power are difficult for defenders to combat when he's fit and in form and his touch and vision are useful for bringing others into play.
His first few months demonstrated he has the ability to perform at the highest level and provide City with the kind of forward play they need to be successful.
But he cut an unhappy figure over the final weeks, and he himself may feel a move is for the best. The lure of playing for the Spanish champions under an exciting manager, who appears to have an ability to galvanise his playing staff, may prove difficult to resist.
If that proves to be the case, City would be well advised to try and bring in a like-for-like replacement, rather than rely on Sergio Aguero, Edin Dzeko and Stevan Jovetic.
Aguero is City's only world-class forward, but after a season which has been disrupted by injuries, over-reliance on him would be foolish. Although the club will be hoping he returns injury-free after this summer's World Cup, having managed just 23 Premier League appearances this season, he needs a top-quality partner.
Negredo's collapse in form and Aguero's setbacks saw Dzeko emerge as City's most prominent striker in the closing weeks of the season, scoring a series of vitally important goals that saw City pip Liverpool to the title.
However, his form has been hit-and-miss since his arrival at City, with the burden of being first choice seemingly too great for him.
Which leaves Jovetic. He is a talented player who offers something different than the other forwards at the club. However, he is one who can definitely be filed under "injury prone" after a series of muscle injuries held him back for much of the season.
This means City would need a replacement were Negredo to leave—a player who can bring the same physicality and goal threat. How likely it is City could do a deal for Edinson Cavani is unclear, but a player of his ilk would fit the bill.
Cavani, when played centrally and paired with another striker, is one of the best in Europe, his form at Paris Saint-Germain only suffering since the system shift that saw him operating wide in a front three. He would cost a sizeable fee, but with PSG surely needing to make sales this summer to comply with Financial Fair Play, it wouldn't be a surprise to see him sacrificed.
Chelsea's Romelu Lukaku, who spent last season on loan at Everton, remains another attractive option. He appears unhappy at parent-club Chelsea and, at just 21, his goalscoring record suggests he has a great future in front of him.
Romelu Lukaku turned 21 a fortnight ago. He's just scored his 82nd career goal. Decent effort.— Daniel Storey (@danielstorey85) May 26, 2014
No. League goals when turning 21: Rooney - 44 Messi - 57 Owen - 55 Shearer - 10 Romelu Lukaku has 65. Hell of a record.— Daniel Storey (@danielstorey85) May 26, 2014
Txiki Begiristain's meticulous planning means City will have a list of potential targets for every position to ensure they are prepared for any eventuality, so if Negredo does decide to leave, expect a replacement to be found swiftly.
Rob Pollard is Bleacher Report's lead Manchester City correspondent and will be following the club from a Manchester base throughout the 2013-14 season. Follow him on Twitter here: @RobPollard_.