The German club are said to be ready to open talks with Chelsea and are willing to pay up to €80 million (£52.5 million) for the 25-year-old, according to Bild (h/t Sport).
Chelsea have already done business with Dortmund this season as they loaned Michy Batshuayi to the club in January. The Belgian scored 10 goals in 14 appearances before his season was ended prematurely by injury.
Dortmund have endured a tough season but would be able to offer Morata Champions League football after finishing fourth in the Bundesliga. Chelsea missed out on qualification for Europe's top competition and will play in the Europa League after ending their season in fifth.
Morata only joined Chelsea from Real Madrid in summer 2017 but has endured a mixed season in the Premier League. He has scored 13 goals in all competitions for the Blues but has struggled to cement a regular place in the team.
Manager Antonio Conte has said it has been a difficult season for Morata, per Goal's Nizaar Kinsella:
Despite his failure to consistently shine there has still been plenty of interest in Morata. Former club Juventus are keen to bring him back to Turin, according to the Gazzetta dello Sport (h/t Marco Gonzalez at AS).
Morata spent two years at Juventus before leaving for Real Madrid in June 2016. However, he has said if the decision had been his he would never have left, per Tifo Football:
The striker's future at Stamford Bridge may also depend on whether Conte continues at the club. The Italian is expected to leave in the summer and has said his future will be clarified after Saturday's FA Cup final against Manchester United, per Sam Dean at the Telegraph.
Chelsea may need to strengthen this summer if they are to challenge for the Premier League title and force their way back into the top four. Morata has not had the impact expected when he arrived from Real Madrid and may well be on the move after just one season.
Dortmund will also be looking to strengthen but Morata's history with Juventus suggests he may find it difficult to turn his former team down if they do come calling.