Everton have seen a second bid for Southampton midfielder Tyler Dibling rejected, talkSPORT understands.
The Toffees have resumed talks with Saints after having an initial £27m bid rejected and offered £35m with a further eight in add-ons.
talkSPORT understands the South coast side want a guaranteed £40m for Dibling.
Everton have also made an approach to Chelsea over signing Kieran Dewsbury-Hall on a permanent deal, with suggestions that £30m could get the deal done.
It has been slow going for the Toffees in the transfer market this summer.
Thierno Barry joined from Villarreal for £27m and Adam Aznou completed an £8m switch from Bayern Munich, but neither have any Premier League experience.
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It led to a worrying admission from manager David Moyes, who said the club are not ready for the Premier League.
“We’re not ready to perform well enough in this tournament. We’re not ready to start the Premier League season,” said Moyes
“I’m not overly concerned [by the results] because I don’t have the players which I need and what I want. And obviously, we’re up against it right from the start.
“We knew before we came [to the US] we were going to be really up against it. So, it was never going to be us coming here and winning [games].”
Everton, who drew 1-1 with Man United overnight in the US, get their Premier League campaign underway against Leeds on August 18.
More Southampton exits
Dibling’s Southampton team-mate Mateus Fernandes is also wanted by a host of clubs including West Ham.
Neither player featured in the Saints’ final pre-season friendly on Saturday.
However, Fernandes’ absence was purely down to illness, the club have confirmed.
Will Still’s side played out a 2-2 draw with Brighton at St. Mary’s Stadium.
Meanwhile, Dibling did feature in a 60-minute behind-closed-doors contest against the Seagulls earlier in the day.
Will Still on transfer rumours
Asked about the teenager’s future after the match, Still told BBC Radio Solent: “If you know Ty, he doesn’t really get that bothered by things, he’s not really affected.
“He played really well in the first 60-minute game this morning.
“He’s been struggling; he didn’t come to Spain with us because he’s got a few niggles. He was back in training this week, and we had to push him for 60 minutes.
“We used the first game for that. But no, he’s fine, it’s just being typical Tyler and just getting on with things.
“I’ve no idea (if he will depart). I think the club have set a price. We’ve got good players and there is interest for good players, which is normal.”
As for Fernandes, the Saints boss added: “There’s noise around him, but he’s a good player. He’s shown his quality over the past year, and there is interest – we can’t lie about that.
“But Matty hasn’t been very well and wasn’t in the building the last three days and wasn’t here today. It’s as simple as that.”
Dibling has two years remaining on his Southampton deal after establishing himself in the side during their relegation campaign.
The England Under-21 international scored twice in 33 Premier League appearances last term.
Fernandes, meanwhile, only joined the club 12 months ago from Sporting Lisbon.
He went on to score two goals and provide four assists from midfield in the league during his maiden season in England.
Watch A Young Tyler Dibling Score 3 Identical Goals In One Game!
However, neither Dibling nor Fernandes were able to help the Saints avoid finishing bottom of the table on 12 points.
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New boss Still will see his side begin the new Championship season at home to newly-promoted Wrexham on August 9.