The 30-year-old left Juventus to join Barca in a €65 million (£59m) deal in June, while Brazilian midfielder Arthur made the move the other way to the Serie A champions.
Juve were also interested signing Jorginho with Maurizio Sarri keen on being reunited with the midfielder he managed at Napoli and Chelsea.
But Juve dropped their interest following Sarri’s sacking after the club were knocked out of the Champions League by Lyon at the start of August.
According to Fabrizio Romano on the Here We Go podcast, Chelsea were very close to completing a deal which involved an exchange between Pjanic and Jorginho.
It’s claimed that Frank Lampard is a huge admirer of Pjanic and was keen for the midfielder to make the move to Stamford Bridge.
However, Pjanic turned down Chelsea’s approach as he favoured a switch to Barcelona.
Jorginho was also linked with a move to Arsenal but the Gunners strengthened their options on deadline day with the signing of Thomas Partey from Atletico Madrid.
Chelsea were also unwilling to let Jorginho move to Arsenal as they did not want to strengthen a Premier League rival.
United completed a £15.4m deal to sign the Brazilian from Porto on deadline day but the Chelsea defender was lined up if the move fell through.