The Toffees are yet to meet Southampton's valuation, which is believed to be around the £45million mark, for the 19 year old academy graduate.
It is anticipated that Dibling will leave St Mary's this summer, with the club needing to offload players, but only if his valuation is met.
Sky Sports first reported that Everton's latest bid of £35million plus £8million in add-ons fell just short of the understood price tag.
Dibling was not involved in Southampton's 2-2 draw against Brighton at St Mary's on Saturday, having played a 60-minute friendly against the Seagulls earlier in the day.
Saints reportedly value Tyler Dibling at £45millionSaints reportedly value Tyler Dibling at £45million (Image: Southampton FC/Matt Watson)
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The England youth international's minutes were restricted due to an injury which forced him to miss the Girona training camp.
Asked about the starlet's future, manager Will Still refused to speculate: "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."