The Chilean is in ongoing contract renewal talks with Arsenal, but there is currently believed to be a gap between demand and offer.
With Alexis' contract up in June 2018, former Manchester City boss Pellegrini - who revealed that the Etihad Stadium outfit missed out on the Chilean due to FFP rules - is eager not to miss out a second time.
The Hebei coach is reported to have offered his compatriot a massive £500,000 a week to lure him to the ambitious Chinese Super League side