Reports have circled recently linking Costa with a move to CSL club Tianjin Quanjin. The mooted deal is believed to be worth £615,000 pound-a-week.
Poyet admits he would happily join Tianjin in the race for Costa's signature – if the league changed its foreign player rules.
Currently, teams are only able to field three non-Chinese players on a matchday. Former Manchester United and Manchester City forward Carlos Tevez is Shenhua's most notable foreigner, with the other two spots currently filled by Nigerian and former Newcastle United striker Obafemi Martins, and Colombian and former Inter Milan midfielder Fredy Guarin.
Speaking to talkSPORT, Poyet said: "I would love to [sign Costa] but it will be very difficult for us because of the quantity [of non-Chinese players] we have got.
"There are three who are playing. There would have to be a massive change to the structure of the club to be able to bring Diego here.
"I don't know if it's going to happen, I would never say 'no, never', but I would say it would be very difficult for him to come here," said Poyet.
"If you asked me in December before they changed the rules, I would have said straight away he was coming. I was 100 per cent sure. No doubt.
"But with the new system, it is special to buy a defender.
"The mentality has changed a lot because they [Chinese teams] are looking for players to make the difference up front - the ones that are going to bring people to the stadium."