The Chinese club are on the hunt for a new manager after deciding against extending the contract of Gregorio Manzano.
They have quickly assembled a list of potential candidates, which included Mancini - who has been out of work since leaving Inter Milan in August.
However, according to Calciomercato, the Italian has rejected Shanghai's offer as he wants another job in Europe.
Mancini was reportedly offered a very lucrative salary by the Chinese side and they had hoped to hold talks this week, but they will no longer take place.