The 21-year-old striker is believed to be Xavi's number one target, though a potential deal to land the in-demand Norwegian will depend on Barca's financial situation next summer.
Another player admired by the Spaniard is Manchester United midfielder Paul Pogba, who has less than eight months remaining on his contract at Old Trafford and is believed to be considering his options.
Xavi would also be keen to bolster Barcelona's defensive options with the signing of Sevilla centre-back Jules Kounde, who was heavily linked with a move to Chelsea over the summer; however, the Blues were unwilling to meet his €80m (£68m) release clause.
The final player on Xavi's shortlist is RB Leipzig playmaker Dani Olmo – a player who came through the ranks at Barcelona and could be available in January if they were to meet his €60m (£50.8m) asking price.
In addition, Manchester City's Raheem Sterling and Bayern Munich's Kingsley Coman are two more players who have been linked with a move to Camp Nou since rumours of Xavi potentially moving to Barcelona surfaced.