Is it permissible to say that someone resembles the Prophet (blessings and peace of Allah be upon him)?

There is
nothing wrong with the Muslim saying that So and so resembles the Prophet
(blessings and peace of Allah be upon him), whether that is physically or in
character, if that is indeed the case with regard to that person. 

It was
narrated that al-Bara’ ibn ‘Aazib (may Allah be pleased with him) said: the
Prophet (blessings and peace of Allah be upon him) said to ‘Ali: “You are of
me and I am of you.” And he said to Ja‘far: “You resemble me physically and
in character.” And he said to Zayd: “You are our brother and our friend
(mawla).” 

Narrated by
al-Bukhaari, 2700. 

Similar things
were said by many of the Sahaabah. 

It was
narrated that Anas ibn Maalik said: No one resembled the Prophet (blessings
and peace of Allah be upon him) more than al-Hasan ibn ‘Ali.

Narrated by
al-Bukhaari, 3752. 

And he said
concerning al-Husayn ibn ‘Ali: He was the closest of them in resemblance to
the Messenger of Allah (blessings and peace of Allah be upon him).

Narrated by
al-Bukhaari, 3748.

Al-Haafiz Ibn
Hajar said:

Those who
resembled the Prophet (blessings and peace of Allah be upon him), other than
al-Hasan and al-Husayn, were: Ja‘far ibn Abi Taalib and his son ‘Abdullah
ibn Ja‘far, Qutham ibn al-‘Abbaas ibn ‘Abd al-Muttalib, Abu Sufyaan ibn
al-Haarith ibn ‘Abd al-Muttalib and Muslim ibn ‘Aqeel ibn Abi Taalib.

Among people
other than Banu Haashim were: as-Saa’ib ibn Yazeed al-Muttalibi, the
great-grandfather of Imam ash-Shaafa‘i, ‘Abdullah ibn ‘Aamir ibn Kareez
al-‘Abshami, and Kaabis ibn Rabee‘ah ibn ‘Adiyy. And these add up to ten.

End quote from
Fath al-Baari, 7/97 

Ibn al-Jawzi
said: Among the Taabi‘een there was a man called Kaabis ibn Rabee‘ah
as-Saami… he resembled him (the Prophet (blessings and peace of Allah be
upon him)). Mu‘aawiyah sent for him and kissed him on his forehead, and he
allocated something to him. When Anas ibn Maalik saw him, he wept.

End quote from
Kashf al-Mushkil min Hadeeth as-Saheehayn, 1/42 

Some of the
scholars mentioned people other than these; anyone who has full knowledge of
the attributes of the Prophet (blessings and peace of Allah be upon him)
will understand that. 

Ibn ‘Abd
al-Haadi said of a man called ‘Abdullah ibn ‘Awaanah al-Maghribi, who was a
contemporary of his: More than one of the shaykhs who had knowledge of the
attributes of the Prophet (blessings and peace of Allah be upon him) told me
that this man, al-Maghribi, was similar in physical appearance to the
Prophet (blessings and peace of Allah be upon him).

End quote from
Subul al-Hadiy wa’r-Rashaad fi Seerah Khayr al-‘Ibaad, 2/117 

Likewise,
resemblance may be in character attitude. 

Hudhayfah ibn
al-Yamaan said: The closest of the people in resemblance to the Messenger of
Allah (blessings and peace of Allah be upon him) in terms of conduct,
humility and dignity, was Ibn Umm ‘Abd. Narrated by al-Bukhaari, 6097. 

Ibn Umm ‘Abd
is ‘Abdullah ibn Mas‘ood (may Allah be pleased with him). 

It was
narrated that ‘Aa’ishah, the Mother of the Believers, said: I have never
seen anyone closer in resemblance to the Messenger of Allah (blessings and
peace of Allah be upon him) in terms of conduct, humility and dignity, or in
the manner of standing and sitting, than Faatimah bint Rasool-Allah
(blessings and peace of Allah be upon him). 

Narrated by
at-Tirmidhi, 3762. He said: This is a hasan saheeh hadeeth. It was classed
as saheeh by al-Albaani. 

The wordsconduct, humility and dignity are close in meaning; what they refer
to is good manners, meekness and calmness, and so on. See: ‘Awn
al-Ma‘bood, 14/87 

End quote from
Mirqaat al-Mafaateeh Sharh Mishkaat al-Masaabeeh, 7/2969 

And Allah
knows best.