Update. There's an official statement from the Swedish government, on the 16 June.
The armed forces are tasked with orientation training for Ukrainian pilots and associated ground crew personnel on the JAS 39. The background is that the Ukrainian armed forces have expressed requests to be able to operationally evaluate the JAS 39 as one of the most urgent measures is to strengthen the Ukrainian air defence with a modern combat aircraft system. https://regeringen.se/pressmeddelanden/2023/06/tolfte-stodpaketet-till-ukraina/
In another statement the defence minister stated that the air force "has no gripens to spare, as all are needed for the defence of Sweden", and that the offer was primarily intended to prepare for a future sale of Gripen to Ukraine. https://www.svt.se/nyheter/utrikes/direktrapport-forsamrat-sakerhetslage?inlagg=bd201131a47d882621ba5dad2679a292
So, Ukraine will be able to train on and evaluate the Gripen, but there is currently no official plan to supply them as part of a military support package. Not to rule it out entirely, just not very likely at this time.