The Netherlands international impressed during a loan spell at the bet365 Stadium last season and revealed at the end of the campaign that he was keen to stay for the long term.
At one stage the transfer looked to be dead in the water, with Crystal Palace reportedly waiting to pounce, but Hughes hopes to have Martins Indi in his ranks by the end of Friday.
"My understanding is we are very close," he told reporters. "All being well, he should be with us today at some point and hopefully we will get that done.
"It's one that's frustrated a lot of people, not least myself, but now it's likely to get done unless there's any last-minute hitches, but we don't anticipate any.
"It's probably going to be a day too late [for the Everton game]. He will have a medical and that takes time, so the thinking is he will be ready to go from Monday."
Martins Indi, who featured 30 times for Porto in the 2015-16 campaign, is thought to be valued at around £7m by the Portuguese giants.