Jesus, who guided Benfica to the Europa League final against Chelsea, is regarded as one of the best coaches in Europe for the work he has done at his current club and Braga over the last few years.
Benfica are in talks about tying down Jesus to a new deal at the Estadio da Luz, but it is thought a number of English clubs are keeping tabs on his situation.
The 58-year-old guided Benfica to the Portuguese title in his first season in charge and the Europa League final was the first European final in 23 years for Benfica.
Jesus has helped transform Benfica's fortunes since taking over in 2009 and the current side are regarded as one of the most attractive and attacking teams across Europe
The Portuguese has helped bring through and develop a number of exciting players at Benfica during his time, including the likes of Ramires and David Luiz and he has a keen eye for talent having been forced to sell his key men and bringing in suitable replacements to fill their voids.
Jesus' work has not gone unnoticed with the likes of Chelsea, Manchester City and Everton, who are all on the look-out for new managers this summer, all believed to have him under consideration.
Sources close to Jesus say the tactician hopes to come to England and continue his management career in the Premier League at some point in the future.