The manager admitted he would like to retain striker Ellis Simms, defender Alex Cochrane and forward Ben Woodburn. They are on loan at Tynecastle Park from Everton, Brighton and Liverpool respectively.
Simms has a contract beyond the summer in England, Cochrane is expected to sign an extension with Brighton, while Woodburn is due to become a free agent. His vast salary could make a permanent move to Edinburgh difficult.
Asked specifically about Simms, Neilson said: “I would like to keep him but, with all the loan players, their parent club will make the decision on it. I would like to keep Ellis here, I would like to keep Cochrane, I would like to keep Woodburn here but their parent club will make the decision.
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“It is out of our hands. We have spoken about it but in general with loan deals, especially coming from England, it tends to be July or even August before we get them in. We need to look at other targets and decide. ‘Do we wait for that one or go for this one?’
Hearts travel to Dundee United on Sunday for their first top-six fixture following the Premiership’s split. Neilson stressed the need to continue momentum after securing European football and reaching the Scottish Cup final.
“We have to continue winning football matches. We have had a meeting with the players and in the last five games we are playing against two teams who are challenging for the title, and three teams that are trying to get the European spot behind us.
“They are all going to be at it and we will need to make sure we are ready for it. We want to continue our form going into the cup final. We need to make sure we don’t start looking at that game and stay focused.
“When you are at Hearts you need to win every game. We will go into the game at Dundee United and put our strongest team out so we can try to win it. Then we will do the same whether it’s Ross County or Celtic, then we will be ready for the final.