The 24-year-old made a big impact on Wearside as they won promotion back to the Championship, scoring 13 goals in 27 games.
Two significant muscle injuries prevented him making an even bigger contribution but there is little doubt about the striker’s potential.
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Broadhead has one year left on his contract at Goodison Park currently, which would mean another loan would appear unlikely at least at this stage.
“We will have a conversation with Everton this week, to see where they are at with it and where we are at with it, and see if that’s aligned,” Speakman said.
“We have to respect the fact that he is an Everton player.
“We have seen him as our player for the year, because we had to get the best out of him but now that the season is finished he unfortunately goes back to being an Everton player.
“Look, he’s had some incredible moments and he’s been an inspiration in many respects in terms of some of the goals he’s scored.
“It has been harder for him of late because of injury but you can’t take away from the fact that he has got all the attributes to go and play at Championship level.”
Broadhead received his first call up to the Wales squad last week, but has withdrawn due to injury as he aims to make a full recovery ahead of pre-season.
As it stands, he will report to Everton to then weigh up his and the club’s next steps from there.
Speakman added that they will ‘investigate’ whether a deal can be done to bring any other loan players from last season back to the club.
Jack Clarke is in a similar situation to Nathan Broadhead with a year left on his Spurs deal.
Leon Dajaku’s loan from Union Berlin has automatically become permanent, though Thorben Hoffmann’s from Bayern Munich has not.
Callum Doyle had a successful first season in senior football on loan from Manchester City, making 44 appearances.
Speakman added that a lot of work had already been done to identify potential loan additions for next season, and that he expects it to be an easier recruitment avenue now promotion has been won.
“We’re really pleased with all our loans, they’ve made an impact at times along the way,” Speakman said.
“We’ll definitely be investigating whether some of those players could come back to us but we have to be respectful of the fact that they are not our players.
“It’s not always easy to turn a loan into a permanent one but if it’s right for everyone, there’s a deal to be done.
“Generally I do think we will find better availability in the loan market, we found it’s not always easy to get a Premier League player to come to League One.
“We have spent a lot of time investigating who could potentially be available and Stuart [Harvey] has got us in a really strong position with the work he has done already. “