Former Chelsea and Tottenham midfielder Poyet is currently the manager of Chinese Super League club Shanghai Shenhua.
Costa, who has scored 20 goals so far in the Blues’ title-winning season, has been heavily linked with an exit from Stamford Bridge over the last few weeks.
The Spaniard received a mega-money offer from China in January but was made to stay by Chelsea boss Antonio Conte and owner Roman Abramovich for the remainder of the campaign.
But his Costa’s long-term future isn’t clear and he could be on his way in the summer.
Poyet says it would tough to bring Costa to his club due to the rule brought in that Chinese Super League teams can only field three non-Chinese players per match.
But he will try and see if he can make the deal happen.
“Well I would love to (sign him),” he said on talkSPORT.
“It will be very difficult, very difficult for us because of the quantity (of non-Chinese players we have), there are already 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.”