The promising 18-year-old is wanted at both clubs after starring in Sporting's B team, with Italian side Lazio also contacting his representatives this month about making a free transfer switch.
Sporting are desperate to retain the academy graduate and have offered Djalo a five-year deal which would also see a £30m buy-out clause inserted into the agreement.
However, City are offering higher wages to entice the youngster to the Etihad and it seems his camp are open to the idea of moving to England, having regularly scouted him over the last 12 months.
West Ham have done likewise, but informed opinion in Portugal is that the pacy Djalo would favour City if he does decide to quit his homeland at the end of the season.
A development fee is likely still payable to Sporting, with City also wanting to maintain good relations in a country where their talent spotters are now particularly active.