Uncertainty has been growing over the striker’s long-term future at Stamford Bridge and Everton have retained a long-standing admiration for the 23-year-old.
They believe he fits the profile of the side they are trying to build and were among Delap’s suitors before he chose to join Chelsea from Ipswich Town last summer.
They continue to view him as a player capable of becoming a key part of their project, but would face competition to sign him.
Newcastle United and Leeds United are believed to be very keen on exploring a move for the player, too.
Sources have confirmed to Flashscore there is a possibility the striker is likely to be allowed to leave, with broader changes expected at Stamford Bridge.
Chelsea are currently searching for a new manager and remain interested in Xabi Alonso, while recruitment plans are also shifting. One of their transfer priorities is to bring in a proven, elite centre-forward.
The club are keen to add more top-level experience and established quality to the squad as part of a wider refresh, and the arrival of a marquee striker would significantly increase their chances of regaining the status they once held in the European game.
Delap has found opportunities difficult to convert into momentum this season, scoring just one Premier League goal from 26 appearances, although only 11 of those came from the start.
Those numbers are a stark contrast to the campaign that earned him his move to Chelsea. Delap scored 12 Premier League goals for Ipswich and emerged as one of the most highly-rated young forwards outside England’s elite clubs.
Despite his struggles, Delap still has admirers within Chelsea and there remains belief in his long-term potential. Everton, though, are of the view that a different environment and greater responsibility could help him rediscover the form that made him one of the league’s most coveted young attackers.
The timing may also suit Everton’s wider ambitions.
The club are eager to make a big statement this summer and are actively exploring several additions. Flashscore has previously reported that Everton are also putting together a proposal to bring former defender John Stones back to the club, highlighting the scale of their ambitions ahead of a significant recruitment drive.
Alongside Delap, Everton are also being linked with FC Midtjylland winger Dario Osorio.
The 22-year-old Chile international is admired by several English clubs and fits Everton’s desire to add greater creativity in attacking areas.
Delap, however, may become one of the most intriguing names to watch this summer.