It was also a busy day concerning the existing squad at the club yesterday after back-up goalkeeper Jack Hamilton signed a new deal that will tie him to the Gorgie outfit until summer 2019.
Hearts, however, are set to cut their losses on the injury-prone Soufian El Hassnaoui having entered discussions to terminate the striker’s contract.
Both Burnley keeper Gilks, who has won three caps, and Sint-Truiden left-back Rherras were shown around the club’s Heriot-Watt training complex this week and Neilson admits he is keen to sign the out-of-contract pair.
Neilson, whose side wrap up an impressive first season back in the Premiership at home to St Johnstone tomorrow, said: “Faycal has been over here and we have spoken to him – but we’ve spoken to loads of players. We’ll look to see how things progress over the next few weeks.
“We get linked with players all the time, players get put to us all the time and we’re always looking.
“It’s important for us we try and bring in good players.”
Asked about Gilks, Neilson added: “Again, I always feel before you sign somebody you have to meet them and speak to them eye-to-eye and see what you think about them.
“I have met a lot of players recently but we can’t sign anyone until 9 June anyway. So there’s nothing we can do.
“But we can definitely source players out who we think might be able to get us to the next step.”
Neilson handed Hamilton his fourth appearance of the season in Thursday’s 1-0 win at Aberdeen and even though the 22-year-old is set to go out on loan next tern, the Hearts head coach has seen enough to award the goalkeeper a two-year contract extension.
Neilson added: “I thought Jack did really well the other night, he came in and commanded his box, he did everything we were looking for him to do. But I still believe he needs to go out and get a year playing at a good level and just get that experience of playing 35-40 games.”
However, marksman El Hassnaoui, who has a year left on his current deal, has been told he has no future at the club after two injury-plagued campaigns restricted the 26-year-old to only ten starts.
Neilson, meanwhile, was thrilled that right-back Callum Paterson was included in Scotland manager Gordon Strachan’s squad for the 29 May and 4 June friendlies against Italy and France.
Neilson insists he has no reservations over the 21-year-old’s physical wellbeing even though Hearts are due to return for pre-season training on 15 June ahead of their Europa League first qualifying round tie 15 days later.
He said: “I was delighted. I spoke to Gordon about it and he asked about our European games but I think Callum being in the squad and hopefully getting some game time is great for the boy.
“He was out for about six weeks recently when he had his shoulder problem so he’s had a break. Fatigue won’t be a problem for him.
“It gets him in that environment, training against good players, playing against good players and hopefully it will let him see what he needs to do to get to the next level.”
Asked if he fears clubs will be attracted to the full-back in the wake of his Scotland inclusion, Neilson added: “That’s football, that’s the way it is at any club in Scotland.
“The good thing for us is that it shows that we can get a guy coming through the academy and get him into the Scotland squad. We’ve got other guys coming through as well, Sam Nicholson, Jordan McGhee, Jack Hamilton, John Souttar and Billy King when he comes back – guys that we hope will take that next step to get into the international team.
“Jamie Walker might be a possibility in time but he’s missed a lot of the season through injury.”
St Johnstone midfielder Murray Davidson says he is looking forward to clocking up a decade’s worth of service in Perth.
The 28-year-old, who signed a new three-year deal on Thursday, said: “Time flies doesn’t it? That’s seven years almost completed. That is quite a long time these days. [But] “I’ve got another three years here now and I’m looking forward to it.”