The 25-year-old has developed into an instrumental figures for the Clarets this term, after establishing himself as a regular in Sean Dyche's side over the last four weeks of last season and is among the players England manager Gareth Southgate is keeping an eye on.
Tarkowski's performances have also attracted interest of some of the Premier League heavyweights, with City and Arsenal understood to be considering a move for the centre-back at the end of the season.
According to The Times, the Clarets have made it clear they would not consider offers in the January transfer window, although they could be open to negotiate a deal for the defender in the summer, as they did last year when they sold Michael Keane to Everton.
Dyche sees Tarkowski as an integral part of the team and is eager to keep the squad intact next month, as Burnley look to build on their remarkable start to the campaign, which has seen them climb up to sixth in the table.
The appeal of a move to City would be obvious for Tarkowski, and not just because Pep Guardiola's men look set to run away with the title this season. The 25-year-old is Mancunian-born and returned to the north west in February 2016 for family reasons, after spending two years at Brentford.
However, Tarkowski's chances of playing regular first team football could benefit from a move to the capital, given City's back four looks a lot more settled than Arsenal's.
Both clubs have been in the hunt for a homegrown centre-back since the summer, when they chased West Bromwich Albion's centre-back. Over the last couple of weeks, however, Manchester United have emerged as the more likely destination for the Northern Irishman, should he opt to leave The Hawthorns.
City are also keeping tabs on Southampton defender and Liverpool target Virgil van Dijk and are also considering a move for Real Sociedad centre-back Inigo Martinez, who was once of interest to Barcelona.
Van Dijk made no secret of his desire to leave Southampton during the summer and even submitted a transfer request in a bit force through a move to Liverpool. Jurgen Klopp's side are believed to be the Dutchman's preferred choice but Southampton are not in the mood to rush to the negotiating table with Liverpool, who apologised to the Saints for the perceived illegal approach in the summer.
Mauricio Pellegrino's men would presumably be more open to doing business with City, though they will no doubt command a fee north of £60m ($80.5m) for the Holland international, who is still on Liverpool's agenda.
Meanwhile, Burnley will be without Tarkowski for the rest of 2017, starting with the home game against Tottenham Hotspur, after the centre-back was hit with a three-game retrospective ban by the FA.
The defender was charged with violent conduct for an alleged elbow on Brighton and Hove Albion striker Glenn Murray during the 0-0 draw at the Amex, an incident which was missed by referee Chris Kavanagh and the other match officials but was captured by television cameras.