Mourinho had wanted to take the former Sao Paulo star to Old Trafford on an initial loan deal with a view to a permanent £40million deal this summer.
According to reports in France, the Ligue 1 leaders could accept a lower fee as the winger has less than two years left on his contract.
Moura has been told he is free to leave PSG during the January transfer window having failed to make a single league appearance for the club in the league following the summer arrivals of Neymar and Kylian Mbappe.
Lucas has scored 45 times in 228 games in all competitions during six seasons at PSG and has won four Ligue 1 titles and three Coupe de France crowns.More news: HP issues voluntary recall involving lithium-ion battery packs
Unsurprisingly, the Brazilian winger has been linked with a move to Manchester United in recent days, but the rumours have been far stronger in 2018 compared to other years.
The Toffees would provide the No. 9 with plenty of service from wide areas, but Mourinho's squad lacks quality and imagination from wing-back to the wingers.
"If we are interested in him, we'll call Juventus".
Brazilian winger Lucas Moura is understood to be high on Jose Mourinho's wish list for January, and is open to joining the Red Devils if the clubs can agree on a deal. All our current options in the wing department are either central attacking midfielders told to play on the wing or strikers such as Anthony Martial and Marcus Rashford being deployed on the wings.