Neilson has revealed the club are aiming to bring the average age of the squad down, while they will likely be targeting free agents north and south of the border.
We have looked at the players under the age of 26 on expiring deals in Scotland and England who could interest the club this summer.
1. Dylan Connolly
There’s one thing Hearts definitely need more of: pace. Dylan Connolly offers that in abundance. Has played as a winger and wing-back for St Mirren and impressed. Photo: Craig Foy - SNS Group
2. Devante Cole
Motherwell’s top scorer from the campaign just past. Really kicked on when Graham Alexander made him the team’s central attacking focal point. Excellent technique, great feet, stealthy movement and good link play. Photo: Ross Parker - SNS Group
3. Jake Doyle-Hayes
A midfielder who can do a bit of it all but is at his best at the base of the midfield. Uses the ball really well, both short and long. A great combative presence and very good at winning the ball back. St Mirren fans are desperate for the club to tie him down to a longer term deal which says a lot. Photo: Craig Foy - SNS Group
4. Jimmy Dunne
A familiar name for Hearts fans and a player who was well liked during his loan spell at Tynecastle where he built up a promising, albeit short-lived, partnership with John Souttar. Would be a huge tick in terms of replacing Christophe Berra, having done so previously. Wages would likely be a stumbling block. Photo: SNS Group Roddy Scott