Alongside ex-Cuikie number two Tony Begg, Milne led the club to their second win in a row, to maintain their perfect start to their East of Scotland League Conference A campaign.
Former manager Johnny Harvey took over at Berwick Rangers earlier this month.
Milne, who left his post as Hibs Ladies boss in March, sighting family commitments, admits having a young family could prevent him from taking over the reins, although he could yet combine with Begg in a joint-manager role.
“I would love to take the job, it’s a no-brainer for anybody, but for me there is commitment issues and I would have to weigh up those options,” said Milne. “It looks unlikely that I will be appointed, just because of those commitment issues. I definitely want the job, it’s just a case if can I take the job, that’s the only thing.
“I left Hibs because of family issues and I’ve got ongoing commitments in the future that would mean missing five or six games, so if I’m trying to preach to the players to turn up and give 100 per cent, and I’m not there myself, it would be hard to get their backing.
“It’s a great club. There’s a good group of players in there who have the potential to go and take it to the next level. Any manager coming in would be very lucky to work with this group.
“We’ve spoken about it [being a joint manager with Begg] and it might be feasible, but Tony has got commitments as well. I think at this stage we might just have to rule ourselves out.”
Penicuik swept aside their local rivals in the first half with a double from striker Wayne McIntosh, taking his tally for the season to 19 goals. Given their dominance, Milne was disappointed they didn’t score more in the opening period, with Lumbert Kateleza, and Ryan Baptie, netting after the interval.
Milne continued: “I think it was disappointing not to come away with more goals. As soon as we got our two in the first half we slackened off and as soon we got our two in the second half we started to slacken off as well.”
Penicuik dazzled Easthouses in the opening period with the visitors unable to get anywhere near them. It took just nine minutes for the hosts to find the net as McIntosh fired in via the crossbar from Baptie’s low cross from the left.
Good work from Arran Ponton sparked Penicuik’s second after 20 minutes. He played in Kateleza who in turn fed McIntosh and he buried the ball low past Steven Hay.
The lethal frontman should have wrapped up his hat-trick on 41 minutes, before Easthouses keeper Hay made a stunning stop to deny Lewis Barr just before the interval.
He could do nothing to stop Kateleza making it three on 62 minutes when he lashed home after a one-two with substitute Wayne Sproule, and Baptie hit the goal of the afternoon – whether he meant it or not – when he sent a free-kick sailing over the head of Hay and into the top corner from wide on the right touchline.
Easthouses boss David McQueenie could be proud of his side’s display in the second half with striker Gary Shearer twice going close. He said: “I changed the system at half-time and we competed well. We were always up against it, but we battled well.
“It’s been a tough run of games for us, and in the next four games we are looking to push on and pick up some points.”
Penicuik Athletic: Cordery, Forbes, Baptie, Young, Hume, MacDonald, McCrory-Irving, Barr, Kateleza (Somerville), McIntosh (Sampson), Ponton (Sproule).
Easthouses Lily: Hay, McIver, Wilson, Hall, Arthur (Tanish), Young (Anderson), Nethery, McDermott, Shearer, Taylor, Elliot.