Enrique won the Champions League, two La Liga titles and three Copa Del Reys during three years at the Nou Camp before opting to leave the La Liga giants at the end of last season to take a sabbatical year away from football.
The former Celta Vigo and Roma boss has emerged as one of the main contenders to take over Conte amid uncertainty over the Italian's future at Chelsea.
Last week, The Daily Telegraph reported that the former Barcelona ace is keen on moving to Chelsea but added that the Spaniard's wage demands could prove to be a stumbling block for the Blues, with alternatives like Thomas Tuchel and Napoli's Maurizio Sarri being much cheaper.
Alonso would not be drawn on those rumours but asked by Cadena Cope about his view on Enrique, he said: "I don't know him very well to be honest. [Is he a good manager?] Yes, without a doubt, during his time at Barcelona he showed that he is a great coach."
Alonso urged his side to improve their attitude to turnaround their current form and secure qualification for next season's Champions League, with the defeat leaving Chelsea five points behind fifth-place Tottenham Hotspur after 29 games.
"I don't think we were at our best," Alonso admitted following the defeat to City. "I begin to think that it is an attitude problem and we have to make things clearer and improve quickly, because we have nine matches left and we want to be in the top four."
Meanwhile, the Spaniard was more optimistic ahead of the next week's Champions League trip to Barcelona, with the Blues hoping to build on the 1-1 draw from the first leg and book a place in the quarter-finals
"We will head to the [Barcelona] with confidence following the first leg. We are eager to produce a good performance although it will be difficult," the ex-Bolton Wanderers full-back added. "We have to put in a perfect performance, defending like in the first leg and not making any mistake."