Mayor Giuseppe Sala made his comments at a press conference after a further 200 migrants had arrived in the city over the weekend, bringing the total number to 3,300, La Stampa reported.
As well as new arrivals transferred to Milan from reception centres across the country, the city is facing the task of accommodating those sent back from the country's borders with France, Austria and Switzerland.
More migrants than beds
This means there are now more migrants than there are beds at the reception centres. There has been huge pressure on Milan's centres, with 400 people staying at the reception hub at the central station which is only intended to accommodate 150.
Several local charities have mobilized to accommodate refugees, including the Jewish community which has accommodated 70 refugees each night at the Holocaust Memorial, near the station.
In the early hours of Sunday morning, the city's councillor for social services, Pierfrancesco Majorino, sent an urgent request to all reception centres in the area and was able to find space for 200 migrants to spend the night, but the challenge to find accommodation space is ongoing.
'No other spaces can be ready quickly'
Sala has suggested the use of former prisons, where there are large amounts of empty space, and adequate security, adding: "This is a possibility because objectively, there are no other spaces which can be ready quickly."
He also said at a press conference that he had "not ruled out" the possibility of accommodating the migrants in tents, though he later issued a statement to confirm that no tent camp was planned for the city, as several Italian publications had reported, but rather that if necessary, some tents would be made available as a first port of call.
Sala added that the situation "is being confronted and will be resolved with good sense and a lot of work".
However, not all of the regional authorities have been as committed to resolving the lack of accommodation. Sala expressed frustration at the resistence of Lombardy's regional president, Roberto Maroni, to the use of the former base camp for the Milan Expo as refugee accommodation. Maroni, a member of the Northern League party, has been vocal in his opposition, saying the refugees are "illegal immigrants" and should be deported.
More and more migrants are arriving in Italy as a final destination rather than simply using it as a transit stop, and many of those in Milan have been turned back at Ventimiglia or Como. La Stampa recently reported that in 2014, just 0.4 percent of arrivals stayed in Italy, a number which swelled to 4.8 percent and this year has reached almost 50 percent of the total number of migrants who have landed in Italy since January.
The average length of stay in reception centres has increased over the past year too, from six days to 20.
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'Ventimiglia will not be our Calais'
Interior Minister Angelino Alfano said on Monday that the Italy-France border town of Ventimiglia “will not be our Calais” following days of tensions over the migrant situation there.
Over the weekend, 200 migrants, who had managed to swim across the border to France, were sent back to Italy. The weekend also saw clashes between police and activist group No Borders, with police turning tear gas on protesters and several members of the group being arrested for weapons possession.
Tensions are also high at Italy's borders with Austria and Switzerland.
Five hundred asylum seekers are camping at the train station in Como - best known as a holiday hotspot favoured by actor George Clooney - after having been turned away at the Swiss border, from where many had hoped to travel on to Germany, Caritas said on Monday. A volunteer at the station said the sudden increase - just two weeks ago there had been 150 migrants - had led to a health emergency, including cases of scabies, according to Il Messaggero.
In April, Austria threatened to build a fence at the Brenner crossing point unless Italy stemmed the flow of migrants across the border, prompting protests from activists. The situation there has been calmer in recent months after hundreds of Italian officers were dispatched to guard the crossing.
Over 94,000 migrants have arrived at southern Italian ports so far this year, while 3,176 have died trying to make the treacherous journey across the Mediterranean, the International Organization for Migrant (IOM) said on Tuesday.