Recent reports suggested that the French defender was a top target for both the Manchester clubs with City's Pep Guardiola planning a January move by meeting Umtiti's release clause, confirmed to be €60m (£53m, $71.6m).
Meanwhile, Jose Mourinho is also looking to bolster his defence and has identified the former Lyon man, whose current contract at Barcelona runs out in 2021.
But despite seeing a former teammate in Neymar leave the club last summer after the oil-rich Paris Saint-Germain met his release clause, Pique is confident that Umtiti will remain at the Camp Nou "for many more years" even if he is met.
"I'm not worried about what clubs might or might not do,'" Pique said, as per Metro. "Umtiti is a great player and we expect him to stay at Barca for many more years and for him to enjoy his football with us.
"To an extent, the buyout clause is made high so that you can't buy the player. As time goes by, that fee doesn't seem so high at all, but the player still has to want to leave.
"We're very happy with Umtiti and I'm sure he's going to stay here for a very long time."
Umtiti joined Barcelona from Lyon in the summer of 2016 and has slowly established himself as the first choice centre-back alongside Pique.
It is believed that Barcelona will open talks with the 24-year-old and his representatives in the coming weeks with regard to a new lucrative deal.
The La Liga leaders are keen to hold on to Umtiti due to Javier Mascherano's impending deal with Chinese Super League club Hebei Fortune as well as to prevent finding themselves in a vulnerable position following Virgil van Dijk's big-money move to Liverpool.