Spalleti admitted that Inter are 'doing what they can' to secure the Croatian's signature, but Lopetegui has 'no doubts' that Modric will continue to be a Madrid player.
Speaking after Inter's 1-0 win over Lyon in the International Champions Cup, Spalletti said (via Marca): "The club is doing what they can to bring it about [signing Modric].
"I am dreaming of it like all the Inter fans, he would be fundamental for any team including ours. We are ready for whatever happens.
"Still there are days to go during the transfer window and I hope something happens."
Such optimism may be flawed as Real president Florentino Perez stated last week that he would not consider selling Modric for anything less than a whopping €750m - equal to his release clause in his contract.
However, Modric is now expected to meet with Perez this week to discuss his future at the club, and Italian journalist Gianluca Di Marzio has stated that Perez will only come to his final decision over a potential sale during the decisive meeting between the pair.
Il Giornale reports (via Football Italia) that Inter are preparing an offer totalling €40m – an initial €15m loan fee, followed by the option to sign him permanently next summer for a further €25m.
For his part, Lopetegui seems unfazed about the transfer rumours surrounding the 32-year-old star.
Throwback to five years ago when Luka Modric was voted La Liga's worst signing.— ESPN FC (@ESPNFC) August 3, 2018
Champions League titles x4
Champions League team of the season x4
Croatian Footballer of the Year x3
FIFA Club World Cup x3
UEFA Super Cup x3
Copa Del Rey
La Liga pic.twitter.com/cSjFc0YIFq
"I talked to him after his excellent World Cup and we entrusted him to return, on the 8th, to start working to see if he can be on August 15 in the first big goal of the season," Lopetegui said, via AS.
"I told him that he is a player that I am passionate about, I love him and he knows it...He will be happy playing football, as he already was, at Real Madrid.
"Luka is a Madrid player and will continue to be, I have no doubts. We have enjoyed it and we will continue enjoying it."