Kanye West claims he and Kim Kardashian West ''can't think'' of a name for their baby daughter.

The couple welcomed their third child - a sibling for four-year-old North and two-year-old Saint - into the world via a surrogate on Monday (15.01.18) and are still struggling to find the right moniker for the tot.

He told TMZ: ''Can't think of a name, know what I'm saying?''

But he seemed pleased when a photographer suggested they name the baby after his beloved late mother, Donda.

When the name was suggested, he smiled and said: ''That's fire.''

It was recently revealed the couple have ''immediately'' rejected a number of big money offers to share the first photos of the newborn because they felt it would be morally wrong to profit from the situation.

According to reports, the 'Keeping Up With the Kardashians' star and the 'Famous' hitmaker were approached by a number of websites and magazines over the course of the last few months, with all offers above $1 million and some going as high as $5 million.

But Kim, 37, and 40-year-old Kanye never even considered the offers as they don't think it is appropriate to take money for the baby pictures, and also value the security and safety of their family above all else.

The pair will wait until they feel the safety of their baby is secured and will then consider releasing images via their own online platforms.

When North was born, the couple waited two months before releasing the first photo of her, and allowed the same time period to elapse before sharing an image of Saint.

Kim and Kanye announced the happy news of the arrival of the ''healthy, beautiful baby girl'' on her own app.

She shared: ''We are incredibly grateful to our surrogate who made our dreams come true with the greatest gift one could give and to our wonderful doctors and nurses for their special care. North and Saint are especially thrilled to welcome their baby sister.''