Sources in Spain believe the LaLiga champions have eyed the ex-Seagulls star as a successor to Robert Lewandowski.
There is a report of contact having already been made last month.
Barcelona understand Chelsea would be reluctant to sell arguably the only player who has been an individual success in their turbulent season.
But the belief in Catalunya is that financial considerations at Stamford Bridge and alack of Champions League football could weigh in their favour.
They are also aware Joao Pedro has a soft spot for Barca having seen compatriots such as Ronaldinho, Neymar and now Raphinha excel for the Blaugrana.
Joao Pedro speaks excellent Spanish and has used the language to communicate with colleagues at times rather than the less widely-spoken Portuguese.
He left Albion for West London in something of hurry last summer to be on board with Chelsea in time for the Club World Cup.
Chelsea paid about £60 million for his services and Barcelona appear aware they would have to find rather more than that to bring him in.
It is not known whether Albion would receive some of any profit Chelsea made on the player.
While Barcelona have been regularly linked with Julian Alvarez at Atletico Madrid, Joao Pedro is seen as a more suitable target in some respects.
These include the transfer fee, his ability to play both the No.9 and No.10 roles and the fact Atleti might be unwilling to sell their star striker to a domestic rival.
Chelsea are struggling to make Europe next season via the league.
But they can secure a Europa League berth if they beat Manchester City in the FA Cup final.
That is a Wembley occasion both Barcelona and Albion, whose own European ambitions might be favoured by a City win, will be watching with interest.