Messi's current contract expires at the end of June and he is free to discuss a move to another club, but media reports on Tuesday suggested an agreement was imminent.
"Talks are ongoing with Messi's people and, as I said, they're going well. We hope to keep making progress. It's not done but we know that Leo wants to stay.
Real Madrid defender Eder Militao had begun to look like an expensive flop midway through his second season but has suddenly turned into the club's most reliable defender.
The Brazilian, a 50-million-euro signing from Porto in 2019, had only made three league starts by the end of March.
Six minutes later, Barca were in front, Griezmann finishing after De Jong timed his run perfectly to meet Alba's floated cross, only for his header to be palmed by Cillessen into Griezmann's path.
Messi scored a spectacular goal that he started in his own half at La Cartuja before rounding off the victory with a strike into the corner for his 31st goal of the season.
It remains to be seen if his seventh Copa del Rey triumph is the last trophy Messi lifts in Barcelona colours but if this was to be a final flourish, the 33-year-old crafted a fitting farewell.
The Barca captain's contract expires this summer and his futures is up in the air having been linked with a move away ever since his attempts to leave the club last summer were unsuccessful.
"I hope it's not (Messi's last Clasico), I want him to stay at Barcelona, it's good for the Spanish league," Zidane told a news conference.
For Real Sociedad, this was a one-off chance and they took it, edging a final that was tight, tense and without clear openings, but one in which the better team were lifting the trophy at the finish.
Lionel Messi scored a stunning equaliser to make it 1-1 on the night in Paris, but his penalty was saved on the stroke of halftime with the scores level, meaning what could have been a blockbuster second half turned into a non-event.
More than the number of misses, it is perhaps the size of the games that they occur in that sets alarm bells ringing.
Lyon boss Garcia then got involved by saying it was rich of Koeman to criticise PSG for talking about the prospect of signing Messi after he had spoken openly of Barca's pursuit of Lyon forward Memphis Depay.
I don't know why PSG are doing this (talking about Messi) but if they want to talk about Leo, they can.
"I discussed resting Leo with him yesterday and we agreed we would bring him on if we needed him. He came on and changed the game, he brought life to our play," he said.
The Catalans pulled off one of the greatest comebacks in the history of the competition by beating PSG 6-1 in a last-16 second leg in 2017 to progress after losing the first leg 4-0.
He had Marcos Llorente's pressing to thank for his equaliser but the second was almost entirely down to him, the 33-year-old chasing down a long punt downfield before tumbling over in the box.
Messi had twice been sent off playing for Argentina, including at the 2019 Copa America, but never in 16 years and 753 matches with Barcelona's first team.
Sociedad, who made a blistering start to the La Liga season but have since faded, ran their hearts out to keep Barca at bay in a tight match before the game opened up in extra time, when both sides came close to finding a winner.
I don't see myself as a coach, perhaps a sporting director to hire players I want or that the club that I'm at needs.
I would like to tell the Barca fans that I'm not sure whether I'll leave or not but hypothetically speaking, I would like to leave in the best way possible.
Pele scored 643 goals in 665 competitive games for Santos, while Messi needed 749 matches to break the record, although he did it in 17 seasons compared to the 19 the Brazil great needed.