Fajardo and club president Angel Haro addressed the ongoing saga during the official presentation of the club's first three summer signings, Facundo Bernal, Fran Garcia and Diego Conde, at the Ciudad Deportiva Luis del Sol.
Ceballos left Real Madrid last month after agreeing to terminate the final year of his contract, becoming a free agent and reigniting hopes of a return to the club where he came through the academy before joining Real Madrid in 2017 for a fee of around €16.5m, going on to win 16 trophies during his time at the Santiago Bernabeu, including three Champions League titles and two La Liga crowns.
"Regarding Dani, first of all, I want to congratulate him on his recent fatherhood, both him and his family, and send a big kiss to the girls.
"As things stand today, there's nothing significant to report. We're working through a roadmap with positions that are priorities for us. Dani's name is there. I know exactly what talking about Dani means for you as media, and for the fans, but I wouldn't focus on Dani or any individual name.
"I think we shouldn't turn transfer markets into soap operas – we need to work on it with the respect it requires, with maximum discretion, with maximum commitment, and on the Dani matter that's as far as I'll go," Fajardo told reporters.
Haro was similarly reluctant to elaborate further on the club's stance.
"As I said in my last appearance, and as Manu has just indicated, ultimately any signing depends on a lot of things, it depends on a whole host of factors: it obviously depends on there being room within the salary limit, it depends on it being a position we need at that moment, it depends on the coach wanting that specific player and not another, it depends on all of those kinds of factors. When those factors align, the signing happens," the Betis president said.
Ceballos, who turns 30 in August, has agreed to forgo the final year of his Real Madrid salary as part of the termination, but any move to Real Betis still hinges on the club finding room for him both within their salary limit and in a midfield already well stocked, following a summer in which the club have prioritised strengthening other areas of the squad ahead of their return to the Champions League for the first time in 21 years.