New manager Jose Mourinho reportedly wants a director of football in charge at the club to help oversee transfers.
Monchi, 47, is credited with masterminding Sevilla's transfer policy over the past 16 years that has helped them compete with Spanish big boys Barcelona and Real Madrid in La Liga.
Italian newspaper Gazzetta dello Sport claim Inter must find £39m to appease UEFA's Financial Fair Play regulations after failing to qualify for the Champions League this season.
Midfielder Brozovic is a £26.6m target, with Arsenal reportedly keen on the Croatia international who joined from Dinamo Zagreb initially on loan in January 2015.
Arsenal are thought to be seeking additional midfielders this summer following the departures of Tomas Rosicky, Mikel Artetea and Mathieu Flamini and have already signed Borussia Monchengladbach's Granit Xhaka.
GETTY
Morata (left), Brozovic and Monchi (top right) may all be heading to the Premier League
Atletico Madrid are also said to be interested in Brozovic but are unwilling to meet Inter's valuation.
And Gazzetta claim Arsenal could make it a double swoop with a £19m offer for Murillo reportedly in the planning.
Per Mertesacker could be sold this summer and Gunners boss Arsene Wenger is thought to be eyeing a centre-back replacement.
Murillo, 24, boasts 17 Colombia caps and joined Inter after a spell at Granada in La Liga.
GETTY
Inter reportedly want £26.6m for Brozovic
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I have a few offers in England and I’m tempted
Alvaro Morata
Morata discusses his future
Alvaro Morata's future remains unclear after the Juventus striker confirmed in an interview that he wants to play in Spain or England next season.
Real Madrid sold Morata to Juve back in 2013 but inserted a £23m buy-back clause.
There are reports the Champions League winners could buy Morata, 23, and then immediately sell him to another club for a profit.
Chelsea are reportedly keen to sign the striker as incoming manager Antonio Conte seeks a partner for Diego Costa - Morata's international team-mate.
Arsenal and Manchester United have also been linked, although the Blues appear to be leading the race of English clubs jockeying for position.
AS
Alvaro Morata held an extensive interview with Spanish newspaper AS
“I think I'm a different player now than I was when I left Real Madrid, a far cry from the little guy who used to run on the Bernabeu with all the enthusiasm in the world," he told AS.
"Above all else, I proved that I can play for a great team.
“I hope everything may be resolved before June 13 because it’s awkward to be here with the national team with a phone in my hand. Let’s see what happens and where I’ll end up playing.
“Of course, returning to Real Madrid is what I’d like best. This is my desire, to win with Real Madrid, but there are some extraordinary players already at the club, and what I want is to play and feel important.
“Next season, I’ll play for the team who give me the greatest opportunities to do that.
“I have a few offers in England and I’m tempted, not just because of the salary. I think the Premier League would be a great achievement for me, given my characteristics.
“This isn’t to say that I want to leave Juventus, a team who I have nothing but kind words for. I’m just saying that going to the Premier League wouldn’t be a step back, on the contrary.
“With all the things that I learned in Italy, having the opportunity to learn something more in England would make me a more complete player, I think.
“I’m 23 and what I want is to develop, to play, to learn from the best. I want a good career.”