But City are ready to compete for the 24-year-old to solve their own problems at the back next season.
Guardiola has been without captain Vincent Kompany for most of the season and has played left-back Aleksandar Kolarov out of position.
There is hope Kompany will make a full recovery but Gibson would add to the competition for Nicolas Otamendi and John Stones.
Gibson and Stoke midfielder Joe Allen in action at the weekendReutersGibson has looked solid dealing with physical strikers like Romelu LukakuGetty ImagesPep Guardiola has put Gibson on a list of summer targets he wantsReuters
Gibson would also bolster their homegrown number of players in the squad, given Joe Hart’s likely departure.
The Boro centre-back’s stats have impressed scouts in a season where Aitor Karanka’s men have scored the FEWEST goals in the Premier League but have been carried by their defence.
Chelsea boss Antonio Conte is also keeping tabs on Gibson as he considers replacements for John Terry come the end of the seasonReuters
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Ahead of last weekend’s action, Boro had conceded less goals than City, with Gibson playing in every game this season.
Guardiola was interested in Holger Badstuber for short-term cover in the January transfer window but the Germany centre-back went to Schalke on loan but will now look at long-term solutions in the summer.
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