However, the Luton boss wants the midfielder to succeed at Kenilworth Road despite a difficult maiden season.
Morrell featured just 11 times for the Hatters in 2020-21 after arriving for an undisclosed fee from Bristol City last summer.
His lack of game-time has alerted Blues head coach Danny Cowley, who's a big fan of the 24-year-old having worked together at Lincoln.
He started all four matches as the Dragons reached the last 16 before crashing out to Denmark.
Speaking to Luton Today, Jones claims to be 'a bit baffled' by talk of Morrell's future after impressing at the Euros.
But having recruited Henri Lansbury and Allan Campbell to bolster his options, the ex-Stoke chief will assess where Morrell stands in the Hatters' midfield pecking order.
Jones said: ‘What I try to do, I don’t have favourites, I have people I like and care about, but at the end of the day the most important thing is winning football matches for Luton Town.
‘All I do is pick the best 11 that I think will give me a result on a Saturday because friendships and looking after people will cost you your job, so I never do that.
‘Addressing the situation, either he’s one of the best two or three midfield players at the club or he needs to be patient, or does something different, or whatever.
‘If someone comes in and wants to buy Joe Morrell then OK we'll look at it, but I've been a bit baffled with people saying this and that.
‘International football, for example, is categorically different from Championship football, categorically, categorically different from Championship football.
‘Now if anyone can tell me that I was unjust in picking Kiernan Dewsbury-Hall and Pelly-Ruddock last year then let me know.
‘But to Joe, I love Joe, I brought Joe here, I want Joe to succeed here and if Joe wants to succeed then he’s got to be one of the best midfield players.
‘We’ve added to the squad, we’ve added greater competition, so we’ll see where he is.
‘Joe did well, he did well in a lot of the games for Wales and we're proud of that as I wanted them to do well and wanted Joe to do well.
‘But Championship football is different, playing in Rome and playing in Baku is categorically different from going to Rotherham away.’
Jones insisted that Morrell has not handed in a transfer request to leave Kenilworth Road.
But he reiterated the Ipswich-born ace’s future will be in his hands if Luton receive an offer they’re willing to accept.
‘The days of transfer requests being handed in, they don’t happen at this football club,’ Jones added.
‘Because at the end of the day, if Joe doesn't want to be here then fine, we’ll look for a solution.
‘But people only hand a transfer request in when they pretty much know they’re going somewhere and they're usually the best player, don’t want to be there, because they know they've got a big-money move elsewhere. ‘That's not the case here,
‘I get on with Joe, we've got a good relationship. If something comes up then we'll put it to Joe and Joe will have a decision – if it's something the club wants to do.
‘If not, he comes back, he works hard and tries his best for Luton.’