Bournemouth aim to build on their highest league finish by making bids worth more than £30m combined for two of Chelsea’s title-winning players, Nathan Aké and Asmir Begovic, once the season has finished.

Both have been on the fringes at Chelsea, with Begovic, 29, acting as Thibaut Courtois’s understudy for two seasons since arriving for £8m from Stoke City. The Bosnian goalkeeper was close to moving to Bournemouth in January, when a deal was agreed in principle, contingent on Antonio Conte’s side securing an experienced replacement. The inability to do so meant the move was shelved.

Begovic, who has attracted tentative interest from a number of other top-flight clubs, would cost Bournemouth around £12m and, barring rival bids, the transfer is expected to go through. Yet the move for Aké is more complicated. The Dutch defender spent the first half of the campaign on loan at the Vitality Stadium and impressed after forcing his way into the side from mid-November, only for his displays to prompt Chelsea to recall him following a 3-3 draw against Arsenal on 3 January.

An inquiry was lodged by Bournemouth over the 22-year-old’s availability as the mid-winter transfer deadline approached, with Aké having struggled to break into the first team at his parent club, yet Chelsea quickly made clear their reluctance to sell. That attitude may not have changed despite the player having made only one Premier League start – against Watford on Monday – and one substitute appearance in the top flight in the second half of the season. He did begin the FA Cup semi-final against Tottenham Hotspur with Gary Cahill ruled out through illness.

There are those within Chelsea who will need some persuasion to part with Aké, even with Bournemouth expected to make an opening bid of around £20m next month. The player, like Begovic, is eager for more regular football and would be prepared to move on, and could be attracted by a return to the Vitality Stadium having enjoyed his time under Eddie Howe.

Bournemouth finished 16th in their first campaign in the elite and, despite a poor run in mid-season, will better that this time. Having won three of their past four games, they would guarantee a top-half finish with a win at Leicester City on Sunday’s final afternoon. Yet there is a recognition they must improve to maintain their status in a competitive Premier League, with a number of last summer’s signings having struggled.