With F1 braced for a major overhaul in two years' time, there had been some concerns that an early release of the plans would give the top teams a big advantage because they could throw early resource at the new regulations.
That is why Horner was behind a push to delay the finalising of the car rules until December, although a subsequent compromise looked set to shift things until October.
However, speaking after the Spanish Grand Prix weekend, Horner said that the original June timeframe is now looking most likely – although there could be revisions to the rules made in October that could deter teams from beginning work too early.
"At the moment, it looks like it should be in June and then inevitably the teams with more resource will look at it earlier than the teams with less resource, which is why I was certainly pushing for it to be released around October. It's more likely to be June and then updated in October."
A majority of other teams were in favour of the delay until October, because they felt it would be better for planning – and stop the top teams getting a head start.
Williams deputy team principal Claire Williams said: "I think if you weigh up those pros and cons, I would rather have the regulations delayed to avoid the bigger teams with their resources being able to get a jump start on those with fewer resources. I think that's probably fairer for everybody. So we don't get an arms race going into 2021. I'm in favour of the delay.
McLaren CEO Zak Brown added: "I think we would prefer October, really more to give them [the FIA] a bit more time,
"I am less hung up on advantage or disadvantage, I would rather make sure that they absolutely land on the best set of rules. What are standard parts? What are listed parts? And June...while they are very far down the road [with the rules], it is around the corner."