Golovin has emerged as one of the stars of the 2018 World Cup, standing out for the host nation in their opening two games of the competition that has seen them seal their progression to the last 16.
The Serie A champions have been so impressed by Golovin that they have made him their No.1 summer target, and have lodged a €20 million (£18m/$23m) offer to CSKA Moscow in an attempt to get ahead of the competition for his signature.
Indeed, Juve have an agreement in place with the player that would see him earn €3m per season, although CSKA are hoping to push the transfer fee higher and are holding out for €25m (£25m/$29m), plus bonuses.
Golovin has also been linked with a switch to Arsenal, with his father having admitted recently that the talented forward has been learning English - it's Juve, though, that are at the front of the queue.
Wilshere, meanwhile, had been linked with a move to Massimiliano Allegri's side, although Goal understands those reports are wide of the mark and the 26-year-old is not currently a target for the club.
The Arsenal midfielder has announced he will be leaving the Gunners after 17 years with the club when his contract expires at the end of the month, although it remains unclear where he will move next.
Juve are already well stocked in the central midfield area, with Emre Can having arrived from Liverpool to join the likes of Miralem Pjanic, Sami Khedira, Blaise Matuidi and Rodrigo Bentancur, and, as things stand, simply don't need Wilshere.
Goal understands Allegri's side, who are still looking to further strengthen their squad with a view to another push for glory domestically and in Europe, are closing in on a move for Valencia full-back Joao Cancelo.
The Portuguese spent last season on loan at Inter but it is their Serie A rivals that are pushing ahead with a €40m (£35m/$47m) deal, with the player expected to undergo medical examinations on Wednesday and agree a four or five-year contract.
Lazio midfielder Sergej Milinkovic-Savic is not considered a realistic target, however, with the Biancocelesti demanding a huge fee of €150m (£132m/$175m) for the player, who is attracting interest from the Premier League.